{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Estimation Supersedes the T-Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC3 v3.6\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-darkgrid')\n",
    "print('Running on PyMC3 v{}'.format(pm.__version__))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model replicates the example used in:\n",
    "Kruschke, John. (2012) **Bayesian estimation supersedes the t-test**. *Journal of Experimental Psychology*: General."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Problem\n",
    "\n",
    "Several statistical inference procedures involve the comparison of two groups. We may be interested in whether one group is larger than another, or simply different from the other. We require a statistical model for this because true differences are usually accompanied by measurement or stochastic noise that prevent us from drawing conclusions simply from differences calculated from the observed data. \n",
    "\n",
    "The *de facto* standard for statistically comparing two (or more) samples is to use a statistical test. This involves expressing a null hypothesis, which typically claims that there is no difference between the groups, and using a chosen test statistic to determine whether the distribution of the observed data is plausible under the hypothesis. This rejection occurs when the calculated test statistic is higher than some pre-specified threshold value.\n",
    "\n",
    "Unfortunately, it is not easy to conduct hypothesis tests correctly, and their results are very easy to misinterpret. Setting up a statistical test involves several subjective choices (*e.g.* statistical test to use, null hypothesis to test, significance level) by the user that are rarely justified based on the problem or decision at hand, but rather, are usually based on traditional choices that are entirely arbitrary (Johnson 1999). The evidence that it provides to the user is indirect, incomplete, and typically overstates the evidence against the null hypothesis (Goodman 1999). \n",
    "\n",
    "A more informative and effective approach for comparing groups is one based on **estimation** rather than **testing**, and is driven by Bayesian probability rather than frequentist. That is, rather than testing whether two groups are different, we instead pursue an estimate of how different they are, which is fundamentally more informative. Moreover, we include an estimate of uncertainty associated with that difference which includes uncertainty due to our lack of knowledge of the model parameters (epistemic uncertainty) and uncertainty due to the inherent stochasticity of the system (aleatory uncertainty)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Drug trial evaluation\n",
    "\n",
    "To illustrate how this Bayesian estimation approach works in practice, we will use a fictitious example from Kruschke (2012) concerning the evaluation of a clinical trial for drug evaluation. The trial aims to evaluate the efficacy of a \"smart drug\" that is supposed to increase intelligence by comparing IQ scores of individuals in a treatment arm (those receiving the drug) to those in a control arm (those recieving a placebo). There are 47 individuals and 42 individuals in the treatment and control arms, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "drug = (101,100,102,104,102,97,105,105,98,101,100,123,105,103,100,95,102,106,\n",
    "        109,102,82,102,100,102,102,101,102,102,103,103,97,97,103,101,97,104,\n",
    "        96,103,124,101,101,100,101,101,104,100,101)\n",
    "placebo = (99,101,100,101,102,100,97,101,104,101,102,102,100,105,88,101,100,\n",
    "           104,100,100,100,101,102,103,97,101,101,100,101,99,101,100,100,\n",
    "           101,100,99,101,100,102,99,100,99)\n",
    "\n",
    "y1 = np.array(drug)\n",
    "y2 = np.array(placebo)\n",
    "y = pd.DataFrame(dict(value=np.r_[y1, y2], group=np.r_[['drug']*len(drug), ['placebo']*len(placebo)]))\n",
    "\n",
    "y.hist('value', by='group', figsize=(12, 4));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step in a Bayesian approach to inference is to specify the full probability model that corresponds to the problem. For this example, Kruschke chooses a Student-t distribution to describe the distributions of the scores in each group. This choice adds robustness to the analysis, as a T distribution is less sensitive to outlier observations, relative to a normal distribution. The three-parameter Student-t distribution allows for the specification of a mean $\\mu$, a precision (inverse-variance) $\\lambda$ and a degrees-of-freedom parameter $\\nu$:\n",
    "\n",
    "$$f(x|\\mu,\\lambda,\\nu) = \\frac{\\Gamma(\\frac{\\nu + 1}{2})}{\\Gamma(\\frac{\\nu}{2})} \\left(\\frac{\\lambda}{\\pi\\nu}\\right)^{\\frac{1}{2}} \\left[1+\\frac{\\lambda(x-\\mu)^2}{\\nu}\\right]^{-\\frac{\\nu+1}{2}}$$\n",
    "           \n",
    "the degrees-of-freedom parameter essentially specifies the \"normality\" of the data, since larger values of $\\nu$ make the distribution converge to a normal distribution, while small values (close to zero) result in heavier tails.\n",
    "\n",
    "Thus, the likelihood functions of our model are specified as follows:\n",
    "\n",
    "$$y^{(treat)}_i \\sim T(\\nu, \\mu_1, \\sigma_1)$$\n",
    "\n",
    "$$y^{(placebo)}_i \\sim T(\\nu, \\mu_2, \\sigma_2)$$\n",
    "\n",
    "As a simplifying assumption, we will assume that the degree of normality $\\nu$ is the same for both groups. We will, of course, have separate parameters for the means $\\mu_k, k=1,2$ and standard deviations $\\sigma_k$.\n",
    "\n",
    "Since the means are real-valued, we will apply normal priors on them, and arbitrarily set the hyperparameters to the pooled empirical mean of the data and twice the pooled empirical standard deviation, which applies very diffuse information to these quantities (and importantly, does not favor one or the other *a priori*).\n",
    "\n",
    "$$\\mu_k \\sim N(\\bar{x}, 2s)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "μ_m = y.value.mean()\n",
    "μ_s = y.value.std() * 2\n",
    "\n",
    "with pm.Model() as model:\n",
    "    group1_mean = pm.Normal('group1_mean', mu=μ_m, sd=μ_s)\n",
    "    group2_mean = pm.Normal('group2_mean', mu=μ_m, sd=μ_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The group standard deviations will be given a uniform prior over a plausible range of values for the variability of the outcome variable, IQ.\n",
    "\n",
    "In Kruschke's original model, he uses a very wide uniform prior for the group standard deviations, from the pooled empirical standard deviation divided by 1000 to the pooled standard deviation multiplied by 1000. This is a poor choice of prior, because very basic prior knowledge about measures of human coginition dictate that the variation cannot ever be as high as this upper bound. IQ is a standardized measure, and hence this constrains how variable a given population's IQ values can be. When you place such a wide uniform prior on these values, you are essentially giving a lot of prior weight on inadmissable values. In this example, there is little practical difference, but in general it is best to apply as much prior information that you have available to the parameterization of prior distributions. \n",
    "\n",
    "We will instead set the group standard deviations to have a $\\text{Uniform}(1,10)$ prior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "σ_low = 1\n",
    "σ_high = 10\n",
    "\n",
    "with model:\n",
    "    group1_std = pm.Uniform('group1_std', lower=σ_low, upper=σ_high)\n",
    "    group2_std = pm.Uniform('group2_std', lower=σ_low, upper=σ_high)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We follow Kruschke by making the prior for $\\nu$ exponentially distributed with a mean of 30; this allocates high prior probability over the regions of the parameter that describe the range from normal to heavy-tailed data under the Student-T distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with model:\n",
    "    ν = pm.Exponential('ν_minus_one', 1/29.) + 1\n",
    "\n",
    "pm.kdeplot(np.random.exponential(30, size=10000), fill_kwargs={'alpha': 0.5});"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since PyMC3 parameterizes the Student-T in terms of precision, rather than standard deviation, we must transform the standard deviations before specifying our likelihoods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    λ1 = group1_std**-2\n",
    "    λ2 = group2_std**-2\n",
    "\n",
    "    group1 = pm.StudentT('drug', nu=ν, mu=group1_mean, lam=λ1, observed=y1)\n",
    "    group2 = pm.StudentT('placebo', nu=ν, mu=group2_mean, lam=λ2, observed=y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having fully specified our probabilistic model, we can turn our attention to calculating the comparisons of interest in order to evaluate the effect of the drug. To this end, we can specify deterministic nodes in our model for the difference between the group means and the difference between the group standard deviations. Wrapping them in named `Deterministic` objects signals to PyMC that we wish to record the sampled values as part of the output.\n",
    "\n",
    "As a joint measure of the groups, we will also estimate the \"effect size\", which is the difference in means scaled by the pooled estimates of standard deviation. This quantity can be harder to interpret, since it is no longer in the same units as our data, but the quantity is a function of all four estimated parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    diff_of_means = pm.Deterministic('difference of means', group1_mean - group2_mean)\n",
    "    diff_of_stds = pm.Deterministic('difference of stds', group1_std - group2_std)\n",
    "    effect_size = pm.Deterministic('effect size', \n",
    "                                   diff_of_means / np.sqrt((group1_std**2 + group2_std**2) / 2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can fit the model and evaluate its output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [ν_minus_one, group2_std, group1_std, group2_mean, group1_mean]\n",
      "Sampling 4 chains: 100%|██████████| 10000/10000 [00:02<00:00, 3495.10draws/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the stochastic parameters of the model. PyMC's `plot_posterior` function replicates the informative histograms portrayed in Kruschke (2012). These summarize the posterior distributions of the parameters, and present a 95% credible interval and the posterior mean. The plots below are constructed with the final 1000 samples from each of the 2 chains, pooled together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1490.4x662.4 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace, var_names=['group1_mean','group2_mean', 'group1_std', 'group2_std', 'ν_minus_one'],\n",
    "                  color='#87ceeb');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the group differences below, we can conclude that there are meaningful differences between the two groups for all three measures. For these comparisons, it is useful to use zero as a reference value (`ref_val`); providing this reference value yields cumulative probabilities for the posterior distribution on either side of the value. Thus, for the difference of means, at least 97% of the posterior probability are greater than zero, which suggests the group means are credibly different. The effect size and differences in standard deviation are similarly positive.\n",
    "\n",
    "These estimates suggest that the \"smart drug\" increased both the expected scores, but also the variability in scores across the sample. So, this does not rule out the possibility that some recipients may be adversely affected by the drug at the same time others benefit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5VhvlItM03Z568nmststXWA/S63vSE+urnmssx5qC7eIG9h2L9TbZFUBavT8femL6AmvanAuw6uB1WPX2NCXZRVqOw+12H38vERERERERERERERFpkEa0i4iIiIiIiIiIiIg0gxLtIiIiIiIiIiIiIiLNoES7iIiIiIiIiIiIiEgzKNEuIiIiIiIiIiIiItIMSrSLiIiIiIiIiIiIiDSDb2N3zMoqcrdmIHWFhARQXFzRVpdrl1QGKgNQGYDKoJbKofOUQVRUV4cd162t5ztLOR+PysGicrCoHCwqB5VBLZWDpanl0Fp1fFv21Y/HW//b8Mb70j11DLqnjsMb70v3dKTG1OPtckS7r6/T7hBspzJQGYDKAFQGtVQOKoO2onK2qBwsKgeLysGiclAZ1FI5WFQOP+WtZeKN96V76hh0Tx2HN96X7qnp2mWiXURERERERERERESko1CiXURERERERERERESkGZRoFxERERERERERERFpBiXaRURERERERERERESaQYl2EREREREREREREZFmUKJdRERERERERERERKQZlGgXEREREREREREREWkGJdpFRERERERERERERJpBiXYRERERERERERERkWbwtTsAEWlYSWU1VUUV5BSWExHkT4CvnouJiIjUV1heRXlVDTVuN92C/PFXfSkiIiJN4Kpxk1dWBUCgrw/B/k4cDofNUYlIR6REu0g7UVRezarEbNbsy2VXRhGphRWHv3MAMaEBjIwN5WwjilP6dlMiQUREOqWyKhdfmFl8tSebXRnFZJdUHv7OxwHx4V0YFRvKGYMimdgnQvWliIiIHCG/tIpVidlsSC5ga2ohGUUVuGrch78PCXBi9AhhTFwY5w7pQd/uQTZGKyIdiRLtIjZLzi/jre+TWLozkyqXm55dAxgVG8olo4LpERFEZXkV2cWVHMgt5bsDeSzflUW3ID9un9yXmSOi8fXRk3YREfF+ZVUu3l5/iPkbUyipdBEfHsjEPuEMiAwmOMAXB5BeVMG+7BJWJWbzSUIGYYG+XDkujtljYgnv4mf3LYiIiIiNdqQXMe/HZFYmZlPlctMtyI+x8WGcMySKyOAAfBxQXl1Dcn4ZuzKKeev7JN78LokRMV257dQ+TOwToZHuInJMSrSL2KS4opq/rd7Poq1p+Dp9uHhENBcO78mw6K6HK+/w8CDy80sPH1PtquH7pHze+i6J332+h/mbUnj2gqEMjAy26zZERERa3co92fzpq0Syiis5a3AUV4yNZUxc6FE7u1WuGtYn5bNwcyqvrz3If35I5pZT+zBnbCy+To1wFxER6UyS88v42+r9fLE7m64Bvlw2KoaLRkQzKCr4mInz7JJKVuzKZP7GFO5auJ3xvcN59KxB9I7o0obRi0hHokS7iA1W783h91/sIaekklmjY7lxYi8iQwKOe5yv04fJ/bpxat8IVibm8NwXe7h+3iYeO3sQ5w/r2QaRi4iItJ3qGjevfLOfeRuSMXqE8PsLhzI6Luy4x/l56svJ/bqxN7uEV1bv5y9f72PJ9nR+fZ7BkJ5d2yB6ERERsZOrxs38TSm8uuYAPg64eVJvrhkfT0hA41JhkcH+XH1SPJePjuXDrWm8vvYg17yzgbnTB3DpyGiNbheRn1CiXaQNVde4+fua/bzzQzKDooL508XDGR7d9M6+w+HgjEGRjIrpyq8+3cVTS01SC8q5+ZQ+rRC1iIhI2yurcvHA4gTWJ+Uze0wsc6f1x+8ERqMPiAzmxUtH8M1e6wH1je9t5q6p/ZkzNlYdZBERES+VW1rJY5/sZMOhAqb078ZjZw8iqhGD2xri7+vDnHFxTB8Uya+Xmfz+8z1sSy3kV2cP0ptyInIEJdpF2khReTUPfZzAj4cKmDU6hvumDWj2Am2RIQH8bfYonllu8o+1B3HVuLn11D5KHIiISIdWUlnN3EUJbEkp4IlzBnPRiOhmn3PqgO6Mig3lN8tM/rxyLwlphTxxjkGAFksVERHxKrsyinjgox3kl1XxxDmDmTm8Z4v0kXt2DeCVy0fyz7UHeeO7JLKKK/jDzGGNHiEvIt5Pvw1E2kB2SSV3L9zG/pxSnj7X4ILhLTfNi6+PgyfPMXA6HLzxXRKBfk5+fnKvFju/iIhIWyqvcnHvh9vZllrIM+cPYcaQHi127vAufrxwyXD+vf4Qf1tzgPTCCp6/eDjhQVooVURExBt8dyCXBz7aQXgXP96YM7rFp4vzcTi4bXJfYsIC+d3ne7h74XZevnwEwf5Kr4kIaAiPSCvLKKrglvc3cyivjBcvHd6iSfZaTh8Hj58zmLONKF5ZvZ+Ve7Jb/BoiIiKtze1288zy3WxOKeSZC4a2aJK9lsPh4PqJvfn9hUPZmVHELfM3k1lU0eLXERERkbb1+Y4M7lucQO+ILvz7mrGtuibLRSOi+f2FQ9mRXsjcRQmUV7la7Voi0nEo0S7SivJKK7lzwVbySqt4dfYoJvXt1mrX8nE4ePKcwYyI6cqTn+1iV0ZRq11LRESkNbyxLokVZhZ3ntaPs42oVr3WWUYUL18+ksyiSm6Zv4WUgrJWvZ6IiIi0nq8Ts7lr/maMHiG8dsUougf7t/o1pw+K5DfnD2FLSgEPfbyD6hp3q19TRNo3JdpFWklxRTV3L9xOWmEFL146gpGxoa1+zUA/J3+6eDihgb48+slOSiv1VF1ERDqGNftyeH3dQS4Y3pPrJsS3yTXHxYfz6uyRFJVXc/v8rWRoZLuIiEiHs+FQPo99spPhsaG8cvlIQgPbbkq4GUN68PBZg1h3II+XVu1ts+uKSPukRLtIK3DVuHn8013syS7huZnDGBsf1mbXjgz255kLhpBaUM7zXyW22XVFREROVFZxBb9etptBUcE8etagNl3Ue3hMqJVsr6jmzgVbyS+tarNri4iISPPszizm/sUJxIV14Y2fnWTLXOmXjYrh6pPimL8plQ82pbb59UWk/VCiXaQVvLpmP9/uz+WB6QOY3L/1pos5mnHx4Vx/ci+WJGTwhZnV5tcXERFpLFeNmyc/20V5lYvfXTiUAN+2b54O6dmVP186nLTCCu7+cBtlmmdVRESk3cstreT+xQkE+zt5+fKRRAS1/nQxR3P31P6c1r8bf161l62phbbFISL2UqJdpIWt2JXJOz8kM2t0DJePibUtjltO6cOw6K4892WiRueJiEi79d7GFH48VMCDZwykb7cg2+IYFx/O7y4ciplZzJOf7cKleVZFRETarSpXDY98vIO8siqev2Q4PbsG2BqP08fBr88bQs+uATz2yU7yy9QHF+mMlGgXaUHJ+WX87vM9jIoN5f7pA2yNxdfpwxMzBlNUUc1L3+yzNRYREZGGHMor47VvDzB1QHdmjuhpdzhMHdCdudMGsCoxh5e/2W93OCIiInIUf/l6H5tSCnlixmCG9uxqdzgAdA305Q8zh5JbWsnTS03cbj20F+lslGgXaSHVNW6e/MwE4Jnzh+DntP9/r4FRwfxsfDyfJmTwQ1Ke3eGIiIgcVuN28+yK3fg5HTxy1sA2nZf9WK4cG8vsMbHM25DM0p0ZdocjIiIi9XydmM38TanMGRfHOUN72B3OEYb27Mq9pw/g2/25LNiSZnc4ItLG7M8EiniJt75LYltaIY+dPYjYsEC7wznspkm9iQ8P5A9fJFLlqrE7HBEREQAWb0tnY3IBc08fQFSIva971+VwOLhvWn/GxoXy2xV7SMwqsTskERER8UgvLOeZ5bsZ0iOEu07rZ3c4DZo9JoZJfSP469f7OJRXZnc4ItKGlGgXaQGJ2SW8+X0S5w7twYwh7euJeqCfkwfOGEhSXplWQBcRkXYhv6yKV1fvZ1x8WLuYMqY+X6cPv5s5jK4Bvjz0cQJF5ZpnVURExG41bjdPLzOpcrn57YVD8bdhAfXGcDgcPDFjMH5OH55aamrdF5FOpH3+VhLpQFw1bn67YjddA3y5f5q987IfzeR+3Ti1XwRvfHeQvNJKu8MREZFO7rVvD1BcUc2DZ7SfKWPqiwz25/cXDiW1oJwnPk7QPKsiIiI2W7gljQ2HCpg7rT+9I7rYHc4x9egawINnDmBbWiHzN6XYHY6ItBEl2kWaacHmVLanFXHf9P6EB/nZHc5R3Xv6AMoqXfxj7UG7QxERkU7MzCxm0dY0Lh8Ty8CoYLvDOaYx8WHcNrkvn25LZ0mC5msXERGxS0pBGS9/s49JfSK4eGS03eE0yrlDejC5Xzde+/YA6YXldocjIm1AiXaRZsgpqeTv3x5gUt8Izm1nU8bU1697EJePiWXR1jT255TaHY6IiHRCbrebF1ftJTTQj1tP7WN3OI1y3YRenNK/G3/6MpEDuao/RURE2prb7ea3K/bg43DwqxmD2u3bcPU5HA4ePmsgbjc892Wi3o4T6QSUaBdphte+PUB5dQ0PTB/QISr7myb1JtDXyWvfHrA7FBER6YTWHchjw6ECbp7Um9DA9vsWWF1OHwd/mjWKAF8fnl5qUq15VkVERNrU8l1Z/JCUz52n9SM6NNDucJokJjSQ2yf3Zc2+XFbuybY7HBFpZUq0i5wgM7OYj7alc+XYWPp0C7I7nEaJCPLnmvFxfLUnmx3pRXaHIyIinUiN280rq/cTGxbIZaNj7A6nSXqGBvLwWYNISC/iPz8csjscERGRTqO4opqXvt7H0J4hXDqqY7Ufal05Lo6BkcH85et9VFTX2B2OiLQiJdpFToDb7ealVXsJDfTlpkm97Q6nSa4+KZ6wQF9eXbPf7lBERKQTWb4rkz1ZJdwxuS9+zo7XBD3biOLMwZG8vu4gidkldocjIiLSKfxz3UFySyp5+KxBOH3a/1vkDfH1cXDf9P6kFlbw3oZku8MRkVbU8Xo5Iu3A2gN5/HiogFtP7dthXn2vFRLgyw0Te/P9wXw2HMq3OxwREekEqlw1vPbtQQZHBTNjSJTd4Zywh88cSIi/L88u341LU8iIiIi0qv05pczfmMIlo6IZHt3V7nCaZULvCE4f0J23vj9EdnGF3eGISCtRol2kiWrcbv6+5gCxYYFcOqpjrHZe36zRMXQP9uet75PsDkVERDqBD7ekkVpQzp1T++HTAdY0OZqIIH/umz6AhPQiFm5JtTscERERr/bXb/YR6Ofkjsl97Q6lRdx9en8qXTX8XWumiXgtJdpFmmjlnmzMzGJuPaVPh3z1HSDQz8m14+P5/mA+29MK7Q5HRES8WEllNW9+l8T4XmFM6hNhdzjNds6QKCb1ieBvqw+QUaQRaSIiIq1h/cE81uzL5caJvYkI8rc7nBbRO6ILc8bFsWR7BrsytGaaiDfqmFlCEZtU17h57dsD9OsWxLlDe9gdTrNcNiqGsEBf/vWdRrWLiEjrmfdjMnllVdx5Wj8cHXg0ey2Hw8HDZw3E5Xbzwsq9docjIiLidVw1bl76eh8xoQFcOS7O7nBa1E2TehPexY8/r9yL261p6ES8jRLtIk3whZnFgdwybp/cp8MuxFIryN/JVSfFsXpfLmZmsd3hiIiIF8ovq2LejymcMSiS4TGhdofTYuLDu3DTpN6s3JPN+oN5docjIiLiVWoXUP/llH4E+HpX2iokwJfbp/RlU0ohX+3JtjscEWlh3vUbS6QV1bjdvL0+iX7dg5g2KNLucFrEFWPiCPZ38rbmahcRkVbw/sYUSqtc3HpqH7tDaXFXnxRPbFggf161l2otjCoiItIiqlw1vL72IEaPEM7uwAuoH8vFI6IZFBXMK6v3U+2qsTscEWlBSrSLNNLqvbnszS7l+pN7deiF3OrqGujLlWNj+XJ3NvtzSu0OR0REvEhxRTXzN6UwfVAkAyKD7Q6nxQX4+nDv6f3Zm13Koq1pdocjIiLiFT7enk5KQTl3TOnrNf3u+pw+Du6Y3Jfk/HKWJGTYHY6ItCAl2kUawe1289b3ScSGBjBjSMeem72+q8bFE+Drw9vrNapdRERazn83p1Jc4eLGib3sDqXVTBvYnfG9wvjHtwcoKKuyOxwREZEOrbzKxRvrkhgTF8qpfTv+AurHMqV/N0bGdOWNdQepqNaodhFvoUS7SCNsOFRAQnoR153cC98OPjd7feFBfswaHcvynZkk55fZHY6IiHiBsioX725I4dR+EQy7yPevAAAgAElEQVTp2dXucFqNw+HgvukDKKqo5p/rDtodjoiISIe2cEsa2SWV3DGlr1csoH4sDoeDO6b0JbO4Um/GiXgRJdpFGmHehmQiuvhx4fBou0NpFdeOj8Pp4+CdHw7ZHYqIiHiBRVvTyC+r4saJve0OpdUNigrh0lExLNicyr6cErvDERER6ZAqq2v4z4/JjO8dzrj4cLvDaRMTekcwvlcYb32fRFmVy+5wRKQF+NodgEh7dyC3lDX7crnllN4dasXz0tJSXn31L3z00Yc8+uiTnH/+zKPuGxkSwPRY+PT13/LtX1JxAMOGjeCee+4nLi6+7YIWEZEOr6K6hv/7IZnxvcIYHRdmdzit6oMP3uPjjxeRnp6Gr38oj2RPZ/5v7z/qKLx9+/byj3+8QkLCdiorK5kw4WTuu+9hunf3jkXWRURETtQnOzLILqnk1+cZdofSImrbCBkZafTsGc1FF13KFVdc/ZP97pjSj5ve28wHm1Lx3fMVixYtIDc3l9jYWK677kauuGKWDdGLyInqOFlDEZu8vzEFP6eDWaNj7Q6l0ZKSDnD99VcB1vzyx1NdXY258EVqfLtwzj0v8N57HxIeHs4DD9xNdXV1a4crIiJe5JOEdLJLKrlxknePZl+69BPeeOM17rvvIZYu/YpLb7iXlLWLeeX/5je4f3FxMXPn/pLg4BDefXchCxYsITg4hMcee7CNIxcREWlfqmvcvLP+EMOjuzKhd8cfzV63jfDZZ1/x4IO/4s03/8HSpZ/8ZN9RsaFM6d+Nf/37X3y4aAHPPPMHli79iptuuo1///tN0tPTbbgDETlRGtEucgxTpoyHCVcTlbOdKy9+lB49evL4479m9+5dvPPOW5SUFDN16nQeeeQJnE4nAF999QXz5v2bpKSDBAQEcNpp07jrrnsJCgoGICFhO3//+1/ZuzcRt9vNiBEjmTv3ocMjxy+/fCazZ8/h4MEDrFr1JQ6HgzPPnMHcuQ/hcDiYO/eXbNmyqcF4r7vuRq6//mZycnKYO/dBJkyYxOLFC497n99/v46MtGTG3/4QS/aUcOu0IO68815mzpzBunVrOO20aS1ToCIi4tWqXTX8e/0hRsaEMr5X4zrKU6aM51e/eprPP1/O1q2b2ryuXbnyS3x8ml7XLlgwnwsuuIhx48YDcPdlZ7J0xQoWLZzPnT+78iej2rdt20xOTja/+MU9hIaGAjB37kOcd950duzYzrBhI5pe4CIiIl7gCzOLlIJy5k7rf0T96S1thNGjx3DBBRfxwQfvct55F/7kuJsmxLL+r19gXHEHQ4cOB2D69LOYPv0swsODyM8vbbnCFpFWpRHtIsdRY37FPXfew2effUVsbByPP/4wycnJvPfeQl577S2+/HIF69Z9C8APP3zPs88+xc9/fhPLlq3kH/94C9PcwUsvPQ9AZWUlDz10D8OHj2TJkhUsWLAEl8vF73//myOu+e67/8cpp0zmm2/W8NRTv+XDD//L2rVrAHjxxb/x1VdrG/xz/fU3AzB27EmccsqURt9jQsI2YmPjuWHqEPLLqvhsRwahoWHExsaRkLC9JYpRREQ6geW7skgrrODGSb2atIjZe+/9H3fccZctde2SJSuOW9du3Lj5iLq2srKSxMTdhzvDAH5OH2acOp6KnGSWJ6Q0cJdWebjdNYe3BAYGEhAQwM6dOxpdViIiIt6kxu3m7fVJ9O8exGkDuv/k+6a0EdatW9vmbYT6/fGG2ggAQ4cOZ+/eRMrLy39aCPnJOKrKWJOYyc+vv5oZM07n5puv44cfvmuJIhaRNqREu8hRuGqsKVd6Dh7HGSePxt/fn1NPPY28vFxuueUOAgIC6devPwMGDOTAgX0AfPjhf5k6dRpTp07D6XQSFxfPjTfexooVS6moKMff35/331/MzTffjq+vLyEhIZx22jR27DgymT1q1BhOO20avr6+nHzyJMLDI9i7d0+r3Wt+fh6hoaGMjQtjaM8Q5m1IocbtJjw8nLy83Fa7roiIeA+32828Dcn07x7E5H7dmnTs5MlTGTRocIepawsLC3G5XIdHpteaOqwPDtz8c+WOw+2I/11vNN27d+eVV14iLy+P0tISXn/9VaqrqykoyG9SeYmIiHiL1Xtz2ZtdyvUTe+HTwEP6prQR3nvvvXbbRggPD6empqbBOj8jIwOA6r3fMXrWPSxa9Cnjxo3noYfmkpR0sFHXFZH2QVPHiBzFt/utBPMpwwYc3hYYGEhERDcCAgIObwsICKSiogKw5kZPTj7EN9+sPOJcbrebrKws4uN7sW7dGt5//z8cOnQIl6sal8uFy3XkCuPx8b2O+BwYGNjwk+8W5nA4uHZ8PL/6dBer9+Ye3iYiInI8Px7KZ09WCU/MGNzkuiM6OubwvztyXev0DGFJKihn6c4MLhweffi74OAQnn/+r7z88otcddWlhIdHcNllV9C//wB8fdUkFxGRzsftdvPW90nEhgVyttGjwX2a0kbYv38/SUkH22UboVbDbSTr4fzw6ZfxaZKL2/wCue22X7Js2ad89tlnzJnz8xa5toi0PrXqRY5iweZUAAb37HrEdh+fo78IEhAQwKWXzubeex9o8PuNG3/kmWee5Je/vIeLLrqMoKAgFi9eyPPP//6I/Y6VoGjMnHBN1a1bdwoLfwTgjMFRRH+zn3k/HqIoP5+xY3/6+p6IiEh9725IoVuQH+cMbbijfCz169b2Xtdec83PcTqdFBYWHPFdfn4+TqcTI74nr689yAyjB/6+/7uXQYMM/vrX14445p133jwiiSAiItJZ/Hgon4T0Ih49ayC+Pg3Xy01pIwQGtv82QljYT9ewiYyMAuCyCQN5cl0xH25J42cTehEdHUNGhhZDFelIlGgXaUByfhnrDuQRADiPUZHX16tXb/bsMY/YVlRUhNtdQ2hoGAkJ2wkKCmLOnGsPf1//NbXjefHFvzVp/8YYMWIU77zzL/LycomI6MZVJ8Xx4rItBCYnM3r02Ba/noiIeJcDOaWs2ZfLraf2IcC3dWcmtKOubWghMsMYSkLCNmbMOO/wtq1btzBkyDBumDaIuxZuZ/G2dK4YGwtY88KuWvUl48aNP9yh3rFjOwUFBYwZM65J8YmIiHiDt78/RGSw/xFvgDVHnz5920V//FhthLqj8Wv17dsPp9NJVfZBJvQewLwNKcwaFU16ehozZpzdpPhExF6ao12kAQs2p+E8yhP1Y5k9+yq2bt3MwoUfUFFRTk5ONr/5zeM8+eSjAMTFxVNeXo5p7qK0tJTFixccnnMtPb1tn1RfffUsVq78AoAJEybSr19/XnrpeQoK8pnWO5DA7YsJiopn/PiT2zQuERHpeN7bmIK/08Hlo1t/ZHZ7qWuvvPIaPvtsCT/+uJ6qqip++OE7li5dwpw51zCxTwTj4sN45dkHmPfePAD8/f155523ePnlP1NWVkZGRjrPP/8HzjvvQnr06NlicYmIiHQEidklrE/K58qxsUe8/dUc1177s3bfRqh1zz138MEH7wEQFhbO+edfxFtv/ZOze1SQU1jMr557gbKyMi6++JIWi0tEWp8S7SL1VLlq+HRHBlMbWPH8eEaMGMVTTz3LRx8t5LzzzuCGG64hLCycp5/+HQCnnz6d8867kLvvvo0rrriY1NQUfv/7F+jbtz/XXXclycmHWuQennvuWc4441RmzJh6xOerrrrs8D5JSQcpLi4GwOl08sc/vkRFRTmXX34R118zi9iufuSfdD0ZxVUtEpOIiHin/NIqPt2RwfnDehIR5N/q12svde2ZZ57NL395L3/842+ZMWMqL7zwHPfc8wDTp5+Fw+HgF1P64irK4rvd/7ves88+R05ODhddNIObbvoZo0aN4YEHHm2ReERERDqS+RtTCPD14ZJRLfeQfsyYMe2+jVArJSWZ/Py8w5/nzn2Q008/g389/ysCP32cTZs28OJLrxIVFdUiMYlI23C43e5G7ZiVVdS4HVtAQ6/ndjYqA/vKYOWebB76eAcvXTqCyf27tfn167Lzv4OMogoufmM9s8fEcv/0Acc/oJXo/wWLyqHzlEFUVFdbViCurec7Szkfj8rB0phyePO7g7z27UHmX38S/bsHt1FkbetE/3u4a8E2dmcV89HNJxPo52yFyNqW/r9QGdRSOViaWg6tVce3ZV/9eLz1vw1vvC877ym/rIoLX/+e84b24FczBrfYeb3l5/TN3hzuX5zA0+caXDO5n1fcU13e8nOqzxvvS/d0pMbU4xrRLlLPx9vTiQz2Z2LfCLtDsVXPrgHMMKL4aFsaheUa1S4iIj9VWV3DB5tSObVfhNcm2Zvjhkm9yC2t4qNtWshMRESk1uKtaVRU13DluDi7Q2mXpvTvxsDIYN5en0RNTbt5jiYijaBEu0gd2SWVrNufywXDex511fPO5Jrx8ZRV1bBoqxIEIiLyU8t3ZZJbWsXV4+LtDqVdGhcfzti4UN754RBVrhq7wxEREbFdtauG/25OZULvcAZG6iF9Q3wcDm6Y2IsDuWV8vjPD7nBEpAmUaBepY+mODFxumDlci5IBGD1CmNA7nPmbUpQgEBGRI7jdbt7fmMKAyCBO7hNudzjt1g2TepNZXMmnCeooi4iIfLUnm8ziSuZoNPsxnTk4iriwQN789oDdoYhIEyjRLuLhdrv5eHs6o2ND6dMtyO5w2o1rToonq7iSL3Zn2R2KiIi0I9vTitidVcLsMbE4HHoL7Ggm9YlgaM8Q/v3DIar1+reIiHRy729MJT48kCk2r4fW3jl9HFw1Lo5Nh/LZklJgdzgi0khKtIt4bE8r4kBuGTNHaDR7Xaf0i6B3RBfmb0y1OxQREWlHFm5JJcjPyblDe9gdSrvmcDi4cWJvkvPL+dzMtDscERER2ySkF7EtrZArxsbho4f0xzVzRDShgb7M25Bidygi0khKtIt4fLw9nUBfH84youwOpV3xcTi4cmys1ShKLbQ7HBERaQfyy6r43Mzi/GE9CPb3tTucdm/qwO4MiAzire8PUePWqHYREemc3t+YQrC/U1O1NlKQv5OrT+7Nqj3ZJOeX2R2OiDSCEu0iQHmVi8/NLM40opQwaMAFw3sS7O/k/Y16ki4iIrBkezqVLjezxsTaHUqH4ONwcMPJvdmfU8qqxBy7wxEREWlz2SWVfGFmceHwnoQEqM/dWNdO7I3Tx8F7GtUu0iEo0S6CtSBLSaWLizRtTIOC/X25eGQ0X+7JJrOowu5wRETERjVuNx9uTWNMXCgDI4PtDqfDOMuIondEF97+Pgm3RrWLiEgns2R7OtU1bi7XQ/om6RkayLlDe/Dx9nQKyqrsDkdEjkOJdhGsSj8+PJCxcWF2h9JuzR4TS02Nm4VbNFe7iEhn9v3BPJLzy7l8tDrKTeH0cXDN+Hh2ZhSzMVmLmomISOdR43azeFs6J/UKo2+3ILvD6XCuOSme8uoaPtyaZncoInIcSrRLp5dWWM6Phwq4cHhPHFqQ5ajiw7tw2oDufLg1nYrqGrvDERERmyzcnEZEFz+mD4q0O5QO5/yhPYjo4sd/fky2OxQREZE2s/5gHqkF5Vw6MsbuUDqkgVHBTOoTwfxNqVSqLy7SrinRLp3e8p2ZAJw7tIfNkbR/c8bFkl9WxfJdmXaHIiIiNkgvLGf1vhwuGhmNv6+akU0V6Odk9phY1uzLZX9Oqd3hiIiItIkPt6YTrof0zXLt+HhySirVFxdp59RDkk5v2a5MRsWGEhfWxe5Q2r3xvcIZEBnE+xtTNL+siEgntHhbOm43XDZKI9JO1OVjYgjw9WHeBo1qFxER75ddXME3idlcOLynHtI3w8l9whkUFcy7G9QXF2nP9FtOOrU9WcXszS7VaPZGcjgcXDk2jj1ZJZpfVkSkk6l21bB4WzqT+3cjNizQ7nA6rIggfy4Y1pOlOzLIKam0OxwREZFWtSQhA5cbLhkZbXcoHZrD4WDO2DgSs9UXF2nPlGiXTm3ZziycPg7OHhxldygdxnlDexAW6Mv8TVoUVUSkM/l2fx45JZVcovlVm+2qk+Kocrn572bVpSIi4r1q3G4Wb01jfK8w+mgR1GabMSRKfXGRdk6J9nbIL/V7HEnr7A7D69W43SzflcmkPhGEB/nZHU6HEejn5JJRMXydmE1qQbnd4YiItDjVww37JCGdbkF+TO4XYXcoHV7fbkGcNqA7CzanUl7lsjscERE5BrULTtx3B/JILazgUk051yLq9sXTCtUXF2mPlGhvh/xS1uE4uMbuMLze5pQCMooqNG3MCbh8dAwO0Eg8EfFKqod/Kq+0ktX7cjlvaE98nWo+toRrx8dTUF7NJwkZdociIiLHoHbBiVu0NY3wLn5MG6hFUFtKbV98gfriIu2SekrSaS3bmUkXPx9OH9jd7lA6nOjQQKYPiuSjbemUaSSeiIjXW7ozE1eNmwtH9LQ7FK8xJi6UYdFdeW9jCq4aLWomIiLeJau4gtV7c5ipRVBbVHRoINM8fXG9FSfS/ui3nXRKVa4avtydzekDI+ni57Q7nA5pzrg4iiqq+WyHRuKJiHi7TxIyGNozhIGRwXaH4jUcDgfXjo8nKa+M1Xtz7A5HRESkRX1Suwiqpo1pcVeOjaOgvJplOzPtDkVE6lGiXTqltfvzKCyv5twhmjbmRI2KDWVIjxDmb0rF7dZIPBERb2VmFLMnq4SZI6LtDsXrTB8USUxoAPM2JNsdioiISItxu90s2Z7O2Pgwekd0sTscrzMmLpRBUcHqi4u0Q0q0S6e0bGcm4V38mNgn3O5QOiyHw8HsMbHszyllY3KB3eGIiEgrWZKQjp/TwTlDouwOxev4+ji46qR4NqcUsj2t0O5wREREWsSWlEIO5Zczc7imnGsNDoeDOWPjSMwuUV9cpJ1Rol06nZLKalbvy+FsI0oLujXTjCFRhAb6aiEWEREvVVldw7KdmZw+IJLQQD+7w/FKF43oSUiAk3k/alS7iIh4hyUJ6XTx8+HMwXpI31pmDIkiLNCX9zem2B2KiNShLKN0Oqv25FBRXaOReS0g0M/JzOHRrEzMIau4wu5wRESkhX1lZlJQXs1MLYLaaoL9fblsVCxf7ckmOb/M7nBERESapazKxRdmNmcNjiLIX+uhtZZAPyeXjorhm705pBeW2x2OiHgo0S6dzrKdmcSGBTIqNtTuULzCrNExuGrcLNqaZncoIiLSwj7clEJUiD8T+0TYHYpXu3JsLA6Hgw826Q0xERHp2L7cnUVplUtru7SBy0ZbC82qLy7SfijRLp1Kdkkl65PyOHdIFA6Hw+5wvEKviC6c0jeCRVvTqXbV2B2OiIi0kOySSr7Zk835w3ri9FGd2Zp6dA3grMGRfLw9nZLKarvDEREROWFLtmfQKzyQMXEa2NbaYkIDmdyvG4u3pVOlvrhIu6BEu3QqX5hZ1LjhnKE97A7Fq8weE0t2SSWrEnPsDkVERFrI8p2ZuGrcXKiFzNrEnHFxlFS6+GR7ht2hiIiInJDk/DI2Jhdw4fBoDWxrI5ePiSW3tIqVe7LtDkVEUKJdOpllOzMZHBVM/+7BdofiVU7t143Y0AD+q0VRRUS8xgozixGxofTtFmR3KJ3CiJhQRsR05YPNqdS43XaHIyIi0mSfJGTgAM4fpoFtbWVS3wjiwgJZsEXTx4i0B0q0S6eRlFdGQnoR52o0e4tz+jiYNTqWjckFJGaX2B2OiIg0U3J+GTvSi7hgZIzdoXQqc8bGkZRXxtr9uXaHIiIi0iQ1bjefJmQwsU8E0aGBdofTafg4HMwaHcOm5AL2qi8uYjsl2qXTWL4rEwcwY4gS7a3hohHR+DsdLNCodhGRDu9zMwuA87WQWZs6c3AkUSH+vLchxe5QREREmuSHpHzSiyqYOUJTzrW1mcOtvvhCjWoXsZ0S7dIpuN1ulu3MZFyvMHp2DbA7HK8UHuTH2UYUS3dkUlyhhdxERDqyFbuyGB0bSmx4F7tD6VR8nT7MHhPL+qR8jUoTEZEOZcn2dLoG+HL6wEi7Q+l0woP8OMuI4rMdGZRWuuwOR6RTU6JdOoWdGcUk5ZVxrkazt6rZY2IprXLx2Y5Mu0MREZETtDe7hMTsEmYMibI7lE7p0pExBPj6MH+TRrWLiEjHUFrpYlViDmcbUQT4Ks1kh1mjYympdLFspxZVF7GTfgNKp7BsZyZ+TgdnDNbT9dY0PCaUoT1DWLA5FbcWchMR6ZA+N7PwccAZg5Vot0N4kB/nDunBZzsyKSirsjscERGR4/p6bzYV1TVaD81GI2O6MjgqmAVb0tQXF7GREu3i9Vw1blaYWUzu143QQD+7w/F6s8fEsj+3lA2HCuwORUREmsjtdvO5mcVJvcKJDPa3O5xOa864OCqqa1i8Ld3uUERERI5r+c4senYNYHRcqN2hdFoOh4NZY2LZk1XC1tRCu8MR6bSUaBev9+OhfHJKKvV0vY2cbUQRFujLf7UoqohIh2NmWlOtzTA0mt1OA6OCGd87nA82pVDtqrE7HBERkaPKK63kuwO5nDMkCh+Hw+5wOrVzh/Qg2N+pRVFFbKREu3i9ZTszCfZ3MrlfN7tD6RQC/ZzMHBHN14nZZBZV2B2OiIg0wYpdWTh9HEwfpKnW7DZnbByZxZWsTMyxOxQREZGj+nJ3Ni43nKP10GwX5O/kgmE9+WJ3FnmllXaHI9IpKdEuXq28ysXKPdlMHxRJoJ/T7nA6jVmjY3C5YUmCXnkXEekoajzTxpzSN4KwLppqzW5T+ncjLiyQ9zdqUVQREWm/lu/KpF/3IAZFBdsdigCXjY6hyuVmyXYtiipiByXaxaut2ZdLSaWL8zRtTJuKD+/ChN7hLN6ajqtGC7GIiHQE21ILSS+q4GxNG9MuOH0cXDE2lq2phexIL7I7HBERkZ9IKyxnc0oh5w3tgUPTxrQLAyKDGRcfxsKtadRoUVSRNqdEu3i1pTsziQz256Re4XaH0ulcNiqG9KIKvjuYZ3coIiLSCJ+bWQT4+jB1QHe7QxGPi0ZEE+Tn1Kh2ERFpl1bsygJgxhA9pG9PZo2OIbWgnHUH1BcXaWtKtIvXKiirYu3+XM4Z0gOnj56ut7XTB3Ynoosfi7dqIRYRkfauxu3mqz3ZnNI3gpAAX7vDEY+QAF9mjujJ52YW2cVa90RERNqX5bsyGRkTSlxYF7tDkTqmD4qkW5AfCzan2h2KSKejRLt4rS93Z1Fd49a0MTbxc/owc0RPVu/NIUvJARGRdm1HehFZxZVaBLUdunJsHK4aNwu36MG1iIi0H4nZJezJKuHcoRrN3t74OX24ZGQ03+7LJbWg3O5wRDoVJdrFay3daS3KMriHFmWxy8UjPYuiaiEWEZF2beWeHJw+Dqb072Z3KFJPr4guTO7fjYVb0qiorrE7HBEREQBW7MrE6YAzByvR3h5dOioGhwMW6Q1zkTalRLt4JS3K0j70jujC+N7hLN6mhVhERNort9vNqsRsxvcKIzTQz+5wpAFzxsWRV1bFil2ZdociIiKC2+1m+c5MJvSJoHuwv93hSAOiQwOZ0r87H29Pp1IP6kXajBLt4pWW7bQ6oucM0bQxdrt0ZDRphRV8p4VYRETapX05pSTllWnamHbs5N7h9O8exPsbU3DrwbWIiNhsW1oRqYUVnKv+drt2+ZgYckurWLkn2+5QRDoNJdrF67jdbpbuzGRMXCixYYF2h9PpTRsYSXgXP72yJiLSTq1KzMYBnD6gu92hyFE4HA6uHBfH7qwSNqUU2B2OiIh0cst2ZhLg68PpA9V2aM8m9okgPjyQBVu0KKpIW1GiXbzO7qwS9ueUcq4WQW0X/H19mDncWhQ1W4uiioi0O6v25DAiJpTIkAC7Q5FjOH9oD8ICfXl/ozrLIiJin2pXDV+YWZzWvxshAb52hyPH4ONwcNmoGDanFJKYVWJ3OCKdgn4ritfwS1lHyNe/Ykrebl7wm8qowf8+5v7OvESC1/wa/9Tvcfs4qe4xhuKpz+CKGAhVpXT9+lH893+O27cLZWNuoWzs7f87NnsHEf+9gKIzX6Ri8CXNC9xVSfC63xGw/3N8SrOo7jaI0vH3UNlvxgmf0lFZTNCPf8F/31KcxWm4QmIoG30z5SOvP7xP4Na36LJjHs6Cg7gdPlRHj6dk4gNU9xx73PMHr/0tQZv+DkDOz9ZRE9oLZ/4+QlY+hF/mFlxd4yme8hRVvacBcPHIaNyb3mLA/91I0VWfUxPe74TvTUREWk5qQTm7Mou5e+rxfy87KgoJWfM0fslrcFQWUd19GCWnPEJ1zIQG9w9bdDn+qd81+F3+JR9Q1WOM99e12/9Dl+3v4CzYj9svhPKBF1Jy6mPg26XBczrzEgn+7jn80tbjqCjEFdqL8qFXUTbuDgL9nDzQ9yCn7LuXbq/l4YoeS9G0546oU7suux3fvD3kXbEUnJozV0REWt76pHzyyqp+Mk1rbX/cN2835UNmU3Tmi8c8j/rjbdMfnzkimn+sPUjqqleZlPs6uVeuUH9cpBVpRLt4hZCVDxG+eDaOshwAenQNILzL0Rd0c5TnEb5oNn7pGyg96U4qBl6Ef/JqQpfdBu4agra8SaC5kPKhc6juMYqQtc/im77BOthVRegX91LZ7+wTqtSdubsJXvssgdvfASD4u+cI2vIG1ZFDKZlwD878fYQuuxVnjnnUc/gUJhP0w4sErX+h4fJY9TBBm/6OOzCCkkkPg48/Xb95nICdHwAQsPMDuq5+Ap/SHEpOfoAK43L8D31N2JJrcZTnHzN+3/SNdNn8Om6fI5/ThXzzOH6ZWymZcB8Aoct/AdVlAPTzzeZXfu/xsuMaqsP6NqqcRESk9a1KtObsnDbw+POzd135IIG7PqCy12mUjb4Zv4wNhH3ycxylDc/7WTb2Doqm//GIP66gHrh9fHGFxHp9XRuY8B+6fv0IjrIcSk6+n6oeIwna9hZdv36swfM5KgoIX3Q5/s8C++8AACAASURBVPtXUD7kCkomPohPWS4h635L4I73obqMq1N+A8Dnkdfjl7GZrt88fvj4gD1LCNi/nKKz/qIku4iItJrluzIJCXByar9uh7fV9sd9ynMadQ71x9uuPx7exY85/as5N+M1ciY8oiS7SCvTiHbxCn4Zmyk8+2X+n707D4+qvNsHfp/ZZ7Lve8hCQgJJIGGXsLsgqIALoNat1aq1rba2te/7/mxta6u1q7VWrfuG4g4uiLIoEGTPAiQhZCNknSSTbZLMfn5/RCIIQoAkzyz357p6WWYmM/c5GXjO8z3PUtPaiYlFDyLuLGuz6w69DkV/K3rmPwZLxgpIDgt6Zz0IWeMPAFA174VLG4Te/N9A2VYKbe3nUDfthSN6Mgx7/wlFXws6l74x5HyStRvaI+ugK18DdUshZEgwz3kYcDmgK30DssqA7kufBJRaSE47/Hb/FbrS1UDqCXezHf3QVq2HrvwtqOsLIEFGX96PTv0wpxXaqo8BAN0X/wuu4GTY4y5CyFuLYCh+DtbMFVA37wEAWDKuRX/unQAAbdXHUPS3Qdlx5DtHJ8JpRcDm+2EbsxCq9lIoe+oHn1I37R0ovuTdDSjV8N/+EFSmI3BEZCNg089hCsnCE00LkH60AzOSQk///kRENKq+qGzH2HA/JIScfoT1cVJfKzTV6+EISoJ5wUCnUmFuhL5sDXRHPkD/xNtP+Rlb0sKT/qwrfRPKPiP6Jt0JV1CS27S1vbN/982bDGNbqzv8HgCgb/r9sIy/Af0530fYS1OgPfwezBc9CFl/cluoMDfBkrYUzpCxsGTdNPBYXysMxc9C1bIfqvBMKO092BP6PfyxeR7mJFVD17j9699PG/y3/h/6Jv8EjoisIZ8zIiKic2GxO/HFkXZcMi4CGtU34zaP98fhtCNw88/P+j6e0h8fqWuE0e6P/6zvcRS7UlGIRVgx5LNGROeDhXbyCh3XfQgotThQ9DgmAogK0KLvDK/XNOwAAKhaihG2/fdQ2M1whKShZ+Hf4YjKheRyQFZ+vVbt8f+67FC1HoBh/5Owpi5B8PvXQNHfDnvsDPQs/MfgRcGJ1Me2QVe2BtqaTyE5LHD6x6B3yr2wZK4amN7VUQWFrRv28AmDn+MIyxj4WWPx1xkLoSt9E9rKdVDYeuDShaJ/4g9gyVwF59evPZFk74fkcgAAZG0gAMAZED9wKKZywNEPW+J86EvfgLphB5QdVVB2H4Vk6YDTLwqOsPHfed78dv8NCnMjuq58HcHvX33yky4HZNXADQ5ZqRs8Z/qSF6BqPYjAMZdgZ8dPof0U0Ey6AX0zHjjDb4iIiEaaqc+Govou/GBG4llfq2o7BEl2wRk6bvAxZ1jmwHMtRWf9eanXCL+C38NpiBocaeVJbW3wt49nCG2tZDMPHJIm8Otj1MDlFwWVxQRVa8ng8mrfnM+MwQ691NcKZU8DNHVbICtUsKZcDnz9eZPGRMLc7ERDr4yxTjsAIODL/4FLGwhV2yGEPZ8Dly4YvdN/BdvYK876uyEiIhqqbdUm9NmduCwz4qTHj/fHj4/YPhv2x0e3P27oKoNFNxnX7VyM0BIVLBkr2B8nGiEstJN3UGphdbhQ1mIGFIBSIZ3x5QrzwEZimmNfwjz3T1A374P+4MsI/PROmG78Eo7QcVAf2wp1ww6oWgoBAM6QVARsvA/2+HxoazbAOuZiWMZfj6CPb4Vh3xPonfk/p3xO8LrrISvUsCUNvNaWOA+QvrnzL1k6AACy+puLAlkT8PVzJsgAAjfcDYW5Efb42bBkroI15bIzTgmXdcFwBKdC1VkFw97H0Z/zfegPvDTwnrILCksnbKmL0TPvUfhv+y1CV88FADiCktG9+AVA43fa91W1FEFf+AzM+b+FKyD2lOcdYeOgbt4HZUcVNMe+GLgwkhTw2/kobInzYKh8H1uj7kJRQzd+ve8J2GOnn1JkICKi0bO1sh0ygHlpZ182RnG8vTqhE3u87Tr+3Jn47XoMCls3eqb/crCdcZe2FhiZttYenQdVeyn0JS/CGZYJlbEQStPANHRFv+mM5yv09blQ2Lrh9I9D9+IXYB8zH5KlA7JCjZTunbgkIhr+7UVwhGdAW/E+NLWbYEuYDc3Rzeha8iJ0ZWsQuOk+tMfnQ9Z9+zYBERHR+dlQZkS4nwZ58d9qW5TntqG6p/THAe/pjy+oXo9H7NdjeWYMMvb9nf1xohHCNdrJa2yvbofV6Rrai7++w9w79Wewjrsa5jkPw+kfA6W5EeqWIvTn/hCugDgEf7AC/l89AmvSJVC3FEGydMCStgySwwJr+nLYE+fCEZoOdf327/4ofRgcEVkDd8alb/2Vk05zQ0CWjz/5zUOaQDgiJsARMWFI6672LPgbXPoIGEpeQNhr+VA37RkcUScrVNDUboL/tt/CGZiA7kufhHnm/0HZ04Cgj24avNg4idOGgM33wxE58aQNXE7UO+PXUPSbELp6LjQ1n6F36s/gX/AH2GOnwRk4MFoyMv8OvO5YAADQnOGcERHRyPuish2xQTqkR5y+Q3ey093Alr/7qRMoOyqhK38LTkMkLBNuGHzc29va3mm/gD0iB5qmXQhdPRf+BQ/DGZo+8MOKM4916V70DHrm/RmAjMD1d0BTuxGyLgR9U++DpuYzPNtzN/xdPSiOvR7+Wx9E77SfQ9HfBkdoOuyJ82D9+vypj69nS0REdIG6LXYU1JhwaUbEWQe2nRX740L64x+qL8OT3bMBsD9ONFI4op28xvpSI5I1qsF+/5nIulCgqxayLmTgAUmCyy8GSnMTpP52uOJmwnTDFqjaSiGr9JCcVgS/txzdi56FZOseeI/jo/rUBih6jaf9HPOs30JXvgZ+u/4Cw+6/w5Y4F5bMVbAlXQIo1XDpwwY+3m4e/BnJ1gUAcBnCIQHonf4L6A++CsP+/8Cw/z+wxU6HJfN6WFOXAOrTr6nriJmC9pt2QNVeBihUcIRlIvy/6ZCVWsi6UBj2/QuS04q+KffBmrZ04DCa90JbswG6w++hf+IPTno/3aHXoDIdhiX1Chh2/XUgp3XgPBiKnoE15XLYE+ei/eadUHVUwOkfD231J1C2l6Pj+o0w7P47ACAhKgLj4iKBdpx1kxciIho5vTYHdtd14LpJsZBO18n8Fpd+YNT78eVQgG/aAZc+4rQ/c5yu9A1Ismug3TphxJvLL9ot2lpgZNpaKJTovPZDKDsqoLB2wx6Zg6CPbgUAOP2iT3+yZBfgtMGeMBt2ALJSg8BNP4Nh7+OwJV2Mvin3wpK+HHJ3A1Z8aMZj5c/AGZSE/ty7oS99Y/B9ZbVh4DitbGuJiGh4bK5og8MlY1Fm5AW/l6f0xwHv6o8vGJ+Et4rqAQ3740QjhYV28gpd/QN3169MCgAaT31e0dsCydYDly4Esj4M9ugpULfsh7p5H2zJlwJOO5TdRwEArqCkgR9S6eGIngw4rQhZswjW9KthS74EmtpNAL6ZZib1tcF1/ALhW/on3YH+SXdAZSyBrnwNtBVroT26GS59OHrm/gm2lEVw6UKh6qwBHBZApYOqrRQA4IieAjUA67hrYR13LZQdVQPvcfhdBG66D65tD6J3xq9hyb7llM/VVG+Aqr0U/eNvhOwXCfWxrZBcdtji8wGFcnAEAZy2wZ+RHJaB/yMPzApQdlQOvCQwcXBZAF3VR6d8lv7AS3DpQmCPnwVZHwq7fgaUndXw2/UYeuY+Apd/LGRt0OA5W5mhAQqARpsegac9a0RENNJ2He2E3Slj7tiwIb3eETEBskIFVXv54GOqtkMAAHv0FACntrXHaY98AACnXy/cDdpa4OxtLWbffcrnnq2tVbUUQt2wE/aYKbDHTodk7Ya6ZR9caj84IrNPuvZwBqdCX/I8/Ar+AGvK5ehZ9PTAcR9vr08YgecKTAQCE/GzhKeRVbsP5QvXIVqhhEsXPNheK/rbAOCbAgYREdEF2lBuRGKIHhmRp66Ffjae2h8HxPfHEZAxbP3xlZk6fLZ/4EYCrxGIRgYL7eQVuj77Pe5VdGC+PNBoqFoPwrDzMQBA34xfwW/no9CVv42+vB+hd+b/oj/nVugPvQZ98XOQlRqo2ssHNlKJmQZHRNZJ7+236y+Q7GaY8x8CANijJ0NW6WEofAqqtkNQddWgd8q9Z8zniMyBOTIH5lm/gbb6M+jK10BlqoAtdTH6s2+B355/IHDDXbBHTxnIpNKhf8KNUJ/wHs6QVPTO/F/0Tn8AmrovoCt/a/Ai4Ns0dV9Af+hVqBu+GthopeR5yJICfZN/AgCwjr0KamMx/Hb/FQprJxS9LVDXb4es0sOWtBAAELp6HgDAdMMX6Jt2P/qm3X/SZ4S+MgPKnnq03/QVXIEJ3zwhuxCw6Wewxc+GNeM6AIAtYTYMRc/Af9tvsMTpBACsNWfipjOeNSIiGinbqtoRoFUhJzZoSK+XdSGwpi+HrvxtBGy8D86AeGiPrIVLHwFr2lUAcEpbCwCK7nooe1sgSwrYI3O+8/1FtrUnGs62Vtl9DP5f/RHOgAT059wGbdXHkByWgfZUpYei+9hgW9t6ZyWsKZfDsPvv0FZ/AtfWB+EKiIO+6FkAgDXpkpM+W9HbjMVN/8JjrpVoq9Lh18mAPT4f+v3/gWHXX6Cp3QSX2g/2mKlnPGdERERDYeyxYt+xLtwxc8xpZ8Id73ur2ssG/usl/fETieqP2+/cOWz98bSSR/B4cAdgAfrj55zxnBHR+WGhnbzC5PoXMVkFoGngz6r2ssFGvm/Gr055vSswEZ3L3oLfjodhKHwKskINy7hrBhvv41TN+6AvehZdV7wyuGO4rAtG96X/gf/2h6AveRGW9OXoy7tnaEGVWljTroQ17UrANVBw7ptyHySnFdryd6Cp2wpHWAZ6Zz04MGLtdBRK2JIWDjTAX7/Ht5nzfwPITmhrNkDdtBeO0HSY5z0Ke/wsAAN39mWlGvoDL8Pvq0cAhRr2mKnom/ozOINThnYs30Ff+DSUHVXouv7ZwcfsifPQO+0X0Je8AEgSPom4A0/VJ+DKfjuC9eozvBsREQ03lyyjoNqEi5JDoDqHNVZ75vwJskIFbdV6SI5+2GOmwjznD4Pt4+ko+loAfL2xmOr006s9oa093XaiZ2trrWlXwWxugv7AS/D76lG4/KJgnvk/6M/90Wk/0hUQh87l7wwWIySnFc6AePTM/v0p67H6b/kVXGEZaNTfgs8PteBH+UmQJv8Eip566Iufh8sQju7Lnh7c0I2IiOhCfH64FTKASzNOv1yc375/nfRn9sfdtz+e65LxZ/sqJFkysOCCPomITkeS5SEsaA2gtbVnaC8cBsHBBnR29o3Wx7kdw55/QqdTw5Q9xMbCSw31e1Dd3ouVL+3Dz+al4IbJ8aOQbPR469+FI61m3PDKfvx8fiquz4s742u99RycK54H3zkHEREBF7i71Pk53s77ynk+E29vhw82deO21UX4w+KMs66zyu/DAHc9D4eNZnzv1f346Zxk3DQ14ew/cIHc9TyMJp6DATwPA871PIxUGz+affWz8cbvhrdeF5zL7+rm1/YDAF75Xt5IRrpg3vj9G+5jcrpkLH9+N+KC9Xjquu+ebTiSvPH3BHjncfGYTjaUdlxxthcQubuPDrZAqZCGZVMWGh1pEf4YHx2AtQeaMNSbfURENDy2VZugkICZSVyb09ONi/RHbnwQ3i5qhMPF9pSIiIZfrakPZS1m9re9hFIh4eqcGOyt60RNu3cVUIncAQvt5NEcLhmflBmRnxyKUINGdBw6B0uzo1HV1odDzT2ioxAR+ZTtVe2YGBuIIC7d5RVW5cWhqduKrVXtoqMQEZEX2lBmhATgknGnXzaGPM9V2dFQKyW8W9woOgqR12GhnTzazloT2nttuGJClOgodI4uHRcBnUqBD0qaRUchIvIZLT1WVLT2YnZqmOgoNEzmpoYhJlCLN/c3iI5CREReRpZlbCg3YnJiMCL8taLj0DAJNWiwMD0CHx1qQZ/t9OvME9H5YaGdPNpHh1oQolcjPyVUdBQ6R/5aFS7NiMBnh43otTlExyEi8gkF1QOjnvNTWGj3FkqFhBW5cSis78Jho1l0HCIi8iKlLWYc67Rg0Xdsgkqe67pJsei1OfFpuVF0FCKvwkI7eazOfju2VrVjUWYkVEp+lT3R0uwY9Ntd+Ly8VXQUIiKfsK3ahLggHZJC9aKj0DBamhUNvVrBUe1ERDSsNpQZoVZKmJ8WLjoKDbPsmACkR/jhnaJG7ptGNIxYnSSP9Vm5EXanzGVjPFh2TACSwwz44ACXjyEiGmkWuxN76jqRnxIKSZJEx6FhFKBTYcn4KGwoN8LUZxMdh4iIvIDTJeOzw62YlRyKQB33dfE2kiTh2kmxONLai5LGbtFxiLwGC+3ksT461IL0CD+kR/qLjkLnSZIkLMuOxqHmHhxp5XR3IqKRtKeuE1aHC7O5bIxXWpkXB7tTxnvFTaKjEBGRF9h3rBPtvTZclhEpOgqNkEWZkfDXKvF2ETdFJRouLLSTR6ps7UVZixlXZkWLjkIXaHFmFNRKCWs5qp2IaERtrzbBoFYiNz5IdBQaAUmhBsxMCsE7xU2wO12i4xARkYfbUG6En0bJ/dC8mF6txBUTorGpog3tvZwRRzQcWGgnj/ThoWaoFBIW8e66xws2qDFvbDjWlxlhdbAwQEQ0EmRZxvbqdkxPCoFGxcs/b7UqLw7tvTZsrODeJ0REdP6sDhc2H2nDvLRw6NRK0XFoBF0zMQYOl4wPDnBGHNFwYE+LPI7N4cLHh1owJzUMwQauFecNlmZHo9viwJYjbaKjEBF5pYrWXhjNNszmqDSvNiMpBGNC9HhzPzc2IyKi87ejxgSz1YlFGRGio9AISwo1YMaYELxb3AQHZ8QRXTAW2snjfFHZhi6LA8tzuGyMt5iaGIzYIB3W8i46EdGI2F7dDgnARckstHszhSRhZV4cSpt7cKCpR3QcIiLyUBvKjQg1qDElMUR0FBoFq/Li0Gq2YVMFB74RXSgW2snjvH+gGbGBWkwbw0bfWygkCUuzorH3WBeOdfSLjkNE5HW2V5swISYAYX4a0VFohC0ZHwV/rRJv7m8QHYWIiDyQ2erAtqp2XDIuAiqFJDoOjYKZySFIDNHjzUJeOxBdKBbayaMc6+jH3rpOLM2OgUJio+9NrpgQBYUErDvITVGJiIZTe68Nh5p6uJmZjzBolFiaFYPNFa1o6bGKjkNERB7mi8o22JwyLuN+aD5DIUlYmRuLg009ONjULToOkUdjoZ08ygcHmqGUgCuzokRHoWEWGaDFrORQfHiohWvDERENo4IaE2QA+SlhoqPQKFmRGwsZwDtFjaKjEBGRh9lQ1orYIB2yYgJER6FRtGRCFPw0nBFHdKFYaCeP4XC68NGhZsxKCUOEv1Z0HBoBS7Nj0N5rQ0GNSXQUIiKvsb3ahEh/DdIj/ERHoVESG6TDnNQwvF/SBIvdKToOERF5iPZeG3bXdWBRRgQkziD3KX4aFa7KisbGijYYOSOO6Lyx0E4eY2u1CaY+OzdB9WKzUkIR7qfBBwe4fAwR0XCwOVzYVduB/JQwdph9zKq8OHRZHFhfZhQdhYiIPMTnh1vhkoHLMrlsjC9akRsLl0vGu8WcEUd0vlhoJ4/xfkkTIv01mJnENWa9lUoh4cqsKOyoMfEuOhHRMCis70Kf3YnZqWw7fU1efBDSIvzw5v4GyLIsOg4REXmADeVGpEX4ISWMs+B8UXywHrNTw/BeSTOsDi7nSnQ+WGgnj9DYZcGu2g5clRUNJXc+92pXZUXDJQMfHuKodiKiC7Wtuh1alQJTEoJFR6FRJkkSVuXFobq9D3vqOkXHISIiN1ff2Y+DTT1YxE1QfdqqvFh09tuxgTPiiM4LC+3kEdYdHCi6Ls3msjHeLj5YjymJwVh3oBkujsAjIjpvsixje7UJUxODoVMrRcchAS7LiESIXs2NzYiI6Kw2lA8UVi/NiBCchESakhCM1HAD3izkjDii88FCO7k9h0vGuoPNmJkcguhAneg4NAqWZUWjsdvKEXhERBfgqKkfDV0WzErmsjG+SqtSYPnEGGyvNqG+s190HCIiclOyLOPTMiNy4wLZ5/ZxkiRhVW4cjrT2Yn99l+g4RB6HhXZye9uq2tFqtuHqnBjRUWiUzEsLR5BOhQ9KuHwMEdH52l5jAgDkp7DQ7suunRgDhULCmkJubEZERKdX0dqLWlM/N0ElAMCizEgE6VScEUd0HlhoJ7f3TlEjogK0mJUSJjoKjRKtSoHLx0fhi8o2mHptouMQEXmkgup2jA3348g0Hxfhr8XF6eH48GAzzFaH6DhEROSGNpQZoVRIWJjOZWMI0KmVWJ4Tg61V7WjssoiOQ+RRWGgnt1bX0Y/ddZ1YnhMNFTdB9SlLs6PhcMlYW8wReERE58psdaCwoRuzOJqdAFyfF4demxMfHWoRHYWIiNyMS5axodyImUkhCNarRcchN3HtpFhIAN7ijDiic8JCO7m1d4sboVRIWJrNZWN8zdhwP2THBOCtvfXchIWI6BztrO2A0yUjn+uzE4AJMYHIjgnEW4UN3GiciIhOUljfBaPZhssyuGwMfSMqQIsF6RFYe7AJvTbOiCMaKhbayW1Z7AMjr+aPDUe4n0Z0HBJgaXY0KlvNKGnsFh2FiMijbK8xIVCnQlZsoOgo5CZW5cXiWKcFBdUm0VGIiMiNrC81wqBWYt5YLtVKJ7thchzMVifWHuDeaURDxUI7ua2PDzSh2+LAtZM4mt1XXTIuEn4aJRt2IqJz4JJl7Kg2YWZSCJddo0EL0sIR6a/hxmZERDTI6nBhY0Ur5qeFQadWio5DbiYrJhC5cYF4Y18DHC7OiCMaChbayW2t3n0MyaEG5MUHiY5Cghg0SizJjsHnh1u5gRsR0RCVNvego9+OfG4iTidQKRW4dlIsdtd1oqqtV3QcIiJyA9uq2tFrc+Ly8VGio5CbunFKApp7rNh0uFV0FCKPwEI7uaWylh6UNHThmokxkCSOxvNlK6bEw+Jw4TM27EREQ7K92gSFBMxMChEdhdzM8pwYaFUKrCnkqHYiIgLWlxkR4a/BlIRg0VHITc1ODcWYED1e495pREPCQju5pXeLmqBXK7FkAu+s+7qcuCCMDffDByVNoqMQEXmEgmoTsmMCEaRXi45CbiZYr8aizEh8UmpEV79ddBwiIhLI1GtDQY0Jl2VEQsml5ug7KCQJN06JR7nRjL3HOkXHIXJ7LLST2+m22PFpuRFXTYyBv1YlOg4JJkkSlmZHo6zFjMNGs+g4RERurdVsRbnRjFkpoaKjkJtalRsHq8OFD7j/CRGRT1t/sBlOl4zLMyNFRyE3t3h8FEINary2t150FCK3x0I7uZ2PDrXA6nDh+qmJoqOQm7g8MxIapYR1LAoQEZ1RQbUJADCb67PTdxgb4YcpicF4u6iRG5sREfmwD4obMDbcD+mR/qKjkJvTqhRYkRuLHTUdqOQ+L0RnxEI7uRWXLOPtokZMjA3EhNhA0XHITQTp1ZifFo71ZUZY7E7RcYiI3FZBjQlRAVqkhhtERyE3tio3Di09VnxxpE10FCIiEuBYRz+KjnVh8XiOZqehuWZiLLQqBV7nqHaiM2KhndzKVzUdqO+0YEVurOgo5GaWZcegx+rAZhYFiIhOy+ZwYdfRDuSnhHIjcTqj/JRQxAXp8OZ+bopKROSL1pe1QJKASzNYaKehCdarcVVWND4tM6LVbBUdh8htsdBObmVNYQPC/TRYkBYuOgq5mckJQUgI1mEtl48hIjqtwvou9NtdmJXM9dnpzJQKCStyY1Hc2I3S5h7RcYiIaBTJsoz1ZUbMTA5DVIBWdBzyIDdMjoNLlrGmsFF0FCK3xUI7uY2jpj58VduBqyfGQKXkV5NOJkkSrsqKxv76Lhw19YmOQ0TkdrZVt0OrUmBqYrDoKOQBrsqKhkGt5Kh2IiIfc6CpB/WdFlw1MUZ0FPIw8cF6zE8Lx7vFjei1OUTHIXJLrGaS23inuAkqhYTlOWzw6fSumBAFpQSsO8hR7UREJ5JlGQU1JkxJCIZOrRQdhzyAv1aFK7Oi8PnhVrRxCjgRkc/4pLQFWpUCl46PFh2FPND3psTDbHVypjnRd2ChndxCn82JDw82Y2F6OML9NKLjkJsK99ciPyUMHx1qgcPpEh2HiMhtHO3oR32nBbNSuGwMDd2K3Dg4XTLeLW4SHYWIiEaBxe7EhnIjFqSFI0CnEh2HPFBWTCBy4wLxxr4G9smJToOFdnILH5e2oNfmxMrcONFRyM0ty4mGqc+ObdUm0VGIiNxGwdf/Juaz0E7nIDFEj1kpoXivpAk2BzvLRETe7svKdpitTlyZFSU6CnmwG6ckoLnHio0VbaKjELkdFtpJOFmW8XZhIzKj/JEVEyA6Drm5GUmhiPTXcKoaEdEJtle3IzXcgJhAnego5GFW5cbB1GfHZ4eNoqMQEdEI+/BQM2ICtZicwP1c6PzNTg1FUqger+w5BlmWRcchcisstJNwe+o6UWPqw4rcWEiSJDoOuTmVQsIVWdHYUWNCU7dFdBwiIuHMVgcKG7oxKzlMdBTyQNPGBCM5zIA39zeys0xE5MWauy3YfbQTS8ZHQcF+N10AhSThlmkJONLai4IazjQnOhEL7STcW4WNCNarccm4SNFRyEMsz46GJAEflHBNWSKiHTUmOF0y5qRy2Rg6d5IkYVVuLA4bzShq6BYdh4iIRsgnpUbIAK7gsjE0DBZlRCI6QIsXd3FUO9GJWGgnoRq7LNhW3Y7lOdHQqvh1pKGJDtThouRQfHCgmRuwEJHP+7KyHSF6NbJiAkVHIQ+1eHwUAnUqvLm/QXQUIiIaAbIs46NDzZicEIS4IL3oOOQFVEoFbpoaj5LGbhQ2dImOQ+Q2WNkkod4paoQE4OqcGNFRyMNcOzEWpj47vqhs7lxrxwAAIABJREFUFx2FiEgYu9OFghoTZqeGQqngNHA6Pzq1EsuyY/BFZRuXZSMi8kJFDd041mnBlROiRUchL3JVVjRCDWq8uOuY6ChEboOFdhLGYndi7cFmzB0bjmhu3kbnaEZSCGIDtXi3uFF0FCIiYfYf60KvzYk5qeGio5CHu25SDCQAbxeyXSUi8jYfHmyGn0aJBem8XqDho1MrcX1eHHbWdqC8pUd0HCK3wEI7CbOh3IhuiwMrcmNFRyEPpFRIWJYTg73HulDb3ic6DhGREF9UtkGnUmD6mGDRUcjDRQfqMD8tHB8caEa/3Sk6DhERDZM+mxMbK1pxcXoE9Gql6DjkZa6dFAs/jRIv7eaodiKAhXYSRJZlrClsxNhwP+TFB4mOQx5qaXY0VAoJ73FTVCLyQbIsY2tVO2YkhUDHjjMNg1V5ceixOvBJaYvoKERENEw2VbSi3+7CFRO4CSoNP3+tCityY7G5og21Jg6AI2KhnYQobujGkdZeXJcbC0nimrJ0fkINGixIC8dHh1pg4eg7IvIx5UYzjGYb5qSGiY5CXiInNhCZUf5Ys78RsiyLjkNERMPgw0MtSAzRY2IcN02nkbEqLw4alQKvcFQ7EQvtJMaawkYEaFW4PDNSdBTycFdPjEGP1YHPD7eKjkJENKq+rGyHQgJmp7DQTsNDkiSsyotDjakPu452iI5DREQXqLa9D4X1XbhyQhQHuNGICTVosCw7Gp+UGdHQ1S86DpFQLLTTqDP2WLHlSCuuyormGnF0wfLig5AcZsC7xVw+hoh8y5eV7ZgYF4Rgg1p0FPIiF6dHINSgxpv7uSkqEZGne/9AE5QKCVdmRYuOQl7u5qkJUErAi7s4qp18GwvtNOreLWmCSwaunRQjOgp5AUmScE1ODA4193CncyLyGQ1d/ahs68VcLhtDw0yjUuDaibEoqDHhKNdaJSLyWFaHCx8fasH8sWEI89OIjkNeLjJAi+U5MfjoUAsauyyi4xAJw0I7jSqbw4UPSpowKyUU8cF60XHISyweHwWdSsFR7UTkM76sbAcAzB3LQjsNv6snxkCtlPBWIUe1ExF5qs1HWtFlcWBZDge40ei4eWoCFBLw4q460VGIhGGhnUbVZ4eNMPXZsSo3TnQU8iIBOhUuy4jEp2VGmK0O0XGIiEbc1qp2pIQZeNOaRkSYnwaXjovAh4ea0WNhu0pE5IneL25CfLAOUxODRUchHxEZoMXy7Bh8yFHt5MNYaKdRI8sy3tjXgOQwA6aNYWNPw+uaSTGwOFz4pLRFdBQiohHV2W9HYX0X5nE0O42g6/Pi0W934f0SzhYjIvI01e29KGzoxvLsGCi4CSqNolumcVQ7+TYW2mnUFDZ0oaK1F9fnxXHHcxp2mVEByIzyx7vFTZBlWXQcIqIRU1BtgksG5owNFx2FvNi4KH9MSwzG6v0NsDpcouMQEdE5+KCkGSqFhCuyokRHIR9z4qj2pm6Oaiffw0I7jZo39jUgSKfC5ZmRoqOQl7p2Yiyq2/tQ1NAtOgoR0YjZVNGKSH8NMqP8RUchL3fztAS099o4W4yIyINY7E58XNqCeWPDEWrgJqg0+m7mqHbyYSy006ho6OrHl5XtWJ4TA51aKToOealLMyLgr1Xi3WJu3kZE3slsdWDn0Q4sTI/gVHAacdMSg5EZ5Y/X9tbD6eJsMSIiT7D5SBu6LQ5cPTFadBTyUVEBWizLjsG6gxzVTr6HhXYaFW8VNkKhkHDtpFjRUciL6dRKLBkfhc1H2tDRZxMdh4ho2G2taofdKWNhOpeNoZEnSRJunpqAuo5+fFnZJjoOERENwXvFTUgM0WNKAvdFI3GOr9X+0q5joqMQjSoW2mnE9docWHugGQvTwhEVoBUdh7zcNRNjYXfKWHeQ09yJyPtsqmhDpL8G2bGBoqOQj5ifFo6EYB1e3lPPPVCIiNxcZVsvihu7sSw7mvuikVBRAVoszYrGuoPNHNVOPoWFdhpxHx1sQa/Niesnx4mOQj4gOcyAyQlBeK+kCS4WBIjIi5itDuysNWEBl42hUaRUSPjelHiUNvdgV41JdBwiIjqDtwoboFUpcOUELhtD4t0yLQESR7WTj2GhnUaUS5axprAB2TEByIrh6DsaHVfnxKCxy4KdtR2ioxARDZtt1e2wOWVczGVjaJQtmRCNUIMaz2yrFh2FiIi+Q1e/HZ+UGrEoIxLBBrXoOESIDtQNjmpv5qh28hEstNOIKqg24VinBavyOJqdRs/8tHCEGtR4p4ibohKR99h0mMvGkBhalQLX58Vhe2U7DreYRcchIqLTWHewGVaHCyvzuC8auY/jo9qf21knOgrRqGChnUbUG/sbEOmvwYI0jr6j0aNWKrAsJwbbq01o6OoXHYeI6IKZrQ58VWvC/LRwLhtDQlw7KRZ+WiVe2s2OMhGRu3G4ZLxV2IjJCUFIi/AXHYdoUHSgDtdMjMVHB5tx1NQnOg7RiGOhnUZMZWsv9tR14rpJsVAp+VWj0XV1TgwUEvBOUZPoKEREF2x7tenrZWMiREchH+WvVeHmGWOwqaINlW29ouMQEdEJtlW1o7nHipW5nElO7ufWaQnQqBT4746joqMQjThWP2nEvPn1RizLcmJERyEfFBWgxfy0cKw72AyL3Sk6DhHRBdlU0YoIfw1y4rhsDIlz20VJ0KuVeP4rjmonInInawobEBOoxezUMNFRiE4R5qfB9Xlx+OxwKyqMXIKOvBsL7TQiOvpsWF/agsXjIxGs50YsJMaK3Dh0Wxz4tMwoOgoR0XnrtTmwo8aEBVw2hgQLMWiwMi8WmypaUcVR7UREbuFIqxn7jnUNzCRX8DqB3NP3piQgQKvCUwW1oqMQjSgW2mlEvFfSBJtT5tQ1EmpSXCDSIvzwVlEjZFkWHYeI6LwUfL1szEIuG0Nu4IbJ8QOj2rmpGRGRW1hT2AitSoGrsqJFRyH6TgE6FW6eGo/t1Sbsr+sQHYdoxLDQTsPO6nDhrcJGzEwKQWq4n+g45MMkScLK3Fgcae1FYUOX6DhEROdlY0Ubwv00mMhlY8gNBOvVWJEbi42HOaqdiEi0zn47Pi0zYvH4SARxJjm5uZV5cQg1qPG3zys4EI68FgvtNOzWl7bA1GfH96bEi45ChMsyIhGoU+GtwkbRUYiIzlmPxYHt1e1YmM5lY8h93MhR7UREbuGDkiZYHS6s4Exy8gB6tRI/mJGI3bUd2H20U3QcohHBQjsNK5cs47W99RgX6Y+picGi4xBBp1ZiaVY0vjjShuZui+g4RETnZGNFK+xOGYvHR4mOQjQo2MBR7UREotkcLrxZ2IhpicEYy5nk5CGWZccgLliHJ7fXcFQ7eSUW2mlYba824WhHP743JR4SR96Rm7h2UixkDOwdQETkSdaXtiApVI/MKH/RUYhOcuPkeOjUCo5qJyISZH1ZC9p7bbh5WoLoKERDplEp8JP5Y1HWYsYXle2i4xANOxbaaVi9trce0QFaXJweLjoK0aDYIB1mp4Th/ZJmWB0u0XGIiIakscuCwoZuLB4fxZvX5HaCDWqszI3DxsOtOGw0i45DRORTXLKMV/cMzCSfxpnk5GGWToxFUqgeTxXUwuniqHbyLirRAch7HGrqRmF9F342LwUqpXfcw2lpacYzzzyJ/fv3wmzuQVZWDn7+8weQmDjmlNfa7XbcfvtN6O3txTvvfAgA6O7uxkMP/S8OHChGcnIqfve7PyEmJnbwZ44dq8P99/8E//3vywgO/u4LpD/+8SHU1x/DU089f8pzv//9gzAaW/Dvf/8XAPDjH/8QJSVFUKm++esdGhqGvLwpuOOOuxEREXnK62RZhkajQXJyKubPX4jly6+DRqM5v5PmplbkxuLLqnZsPNyKJRO4BAMRub/1ZS0ABvaa8Gae0NY+8MCv0NDQyLb2W26aGo93i5vw5LYa/OuabNFxiIh8xraqgZnkDy/O8Pqb8ed2nWDDLbesYp/czamUCtw1Kwm//rAMn5YZ2T8nr+Id1VByC6/trYe/Voml2dGiowwLp9OJX/3qPphM7XjuuVewbt1nGD8+C/ff/xNYrdZTXv/ii8+ipaX5pMfefPM1qFQqfPzxJowbl4nnn39m8DmXy4U//ekh/PSnPz9jg34+Lr74MmzevAObN+/Apk0F+Oc//4Ompkb86lf3weVynfK6LVu+wptvvo9bbvkBNmz4BHfd9X309PQMaybRpiYGIznUgDWFDVwLjojcnizL+KTUiNz4IMQG6UTHGTFsaz27rQ3UqXHb9AR8VduBvXXc1IyIaLS8uucYYgK1WDguQnSUEXWu1wlPPfUUrxM8xPy0cGRE+uO/O2ph46xz8iIstNOwqO/sx+Yjbbg6JxZ+Gu+YKFFXdxRVVZW4/fa7EB4eAYPBgNtvvwsOhwPbt2896bXl5WV47723sXLljac8PmPGLGg0Glx00SyUlh4cfG716leQkDAG+flzR/Q4JElCfHwC7rzzHhw5UoG6uqOnfV1ISChmzpyFJ554Bj09PXjmmSdHNNdokyQJ1+XGoqzFjINN3nvBQkTeobS5B3Ud/Vic6d2j2dnWen5be92kWET6a/DvbdzUjIhoNBQ3dKG4sRs3To6HSuHdo9nP9TrhzTff4HWCh1BIEn48OxmN3Va8U9woOg7RsGGhnYbFG/saoJAkrMqLPfuLPcTxKXgn3m1WKBQIDAxEeXnp4GN2ux1/+tND+OEPf4SoqOjTvgcAOJ0uKBQDf+Wqqyvx0UfrcOmll+Puu7+PW2+9AatXvzqShwOnc+A4Tpy+djp+fv5YvvwabNz46UnH7g2WjI+Cn0aJNYUNoqMQEZ3RJ6VGaJQSFqZ790g1trWe39bq1ErceVESDjX3YMuRNtFxiIi83qt76hGkU+EqL5lJfibnep3w05/ey+sEDzI9KQQzxoTg+Z116LbYRcchGhYstNMFM/XZsPZgMxZlRiLCXys6zrBJSEhESkoqnnvuabS0NMNqteDdd9egoaEeXV3fTI9+4YX/Ijg4BMuXX3vKe2RlZWPnzgJYrVYUFGxFdvZEOBwO/PGPv8P99z+Af//7n1i27Fo88cQzWL36FVRXV35nnoMHS7BgwUWn/G/jxg1nPA6Xy4W6uqN45pl/Y9KkPMTFxZ/12MeMSYbZbD7pOL2BQaPElVnR2FTRhjbzqVMNiYjcgcPpwmeHWzEnNQwBOu+YJfZdPKWtXb/+kzMeh6+3tYsnRCE51IAnt9fCwU3NiIhGTG17H76sasd1k2KhVytFxxlx53qdsHLlqlPew9P75B0dHWd9rSf7yZxk9FgceGnXMdFRiIaFd/feaFSs3tcAm8OFW6YliI4yrJRKJR599O94/PG/4rbbboROp8OiRUswffpMKJUDf3XKy0vx/vtv44UXXj/tJjQrVlyPP/zhN1i69DKMHZuO3/72Ybz88vOYMCELEyZkobKyAvn5c+Dn54+cnEkoKipESsrY0+bJyso548YrJ9q4cQO++GLT13+SEB4ejunTL8Ltt985pM1ynE7n4DnwNismxWLN/ga8U9yEu2YliY5DRHSKr2o70Nlvx+XjvX9jKE9pax955CE0NJw8rZlt7TdUCgn3zE7CL9aWYt3BZlydEyM6EhGRV3ptbz20KgVW5HrPTPIz8ZTrhJHsk6tUSnjzymzpkf5YPCEKawobcF1uLGICvXdvIvINLLTTBem22PFOUSMWpkcgKdQgOs6wi42Nw5///I+THrv99puRnp4Bu92OP/7xIdxxx92IjY077c/7+fnj0Uf/Pvjn8vIybNmyEc899+rgHXi93vD1f3Xo7u4altwXX3wZfvObP5z3z1dUlCMsLByBgUHDksedJIToMSc1DO8UNeLWaQnQ+cBIECLyLJ+UGhGsV+OipBDRUUYF21rvaGvnpIYhJzYQz+44isszI31ipCUR0Whq7rbg49IWLMuORohBIzrOqPH164SgoGB0dvYNSyZ3dddFY7DxcCue2l6L3y/OEB2H6IJw6Ri6IG8VNqLX5sRt071rNPtxW7ZsxNGjtYN/bmtrw5Ejh5GXNwUHD5agpqYaL7zwXyxZshBLlizEP/7xFxiNLViyZCFKSopOei+bzYZHHvkdHnjg/0Gn08HPzx8A0NPTDQDo7OwafEykrq5OrFv3PhYvvlJ0lBFzw5Q4dFkc+KTMKDoKEdFJzFYHtlW349JxEVApfeMyjW2td5AkCT+ZnYy2Xhte21MvOg4Rkdd55et/W71tJvnZnMt1Qn7+RbxO8EDRgTqsyovD+jIjDreYRcchuiAc0U7nrc/mxJv7G5CfEor0SPGN0Uj4+ON1sFgs+OMfHwMAPPLI7zFpUh6ysyfCZrPhvfc+Pun1W7ZsxJo1q/H00y8gOPjkkYjPPvsUpk+/CNnZEwEA/v7+SE5OwebNG5GfPwcHDxbjrrvuGZ0DOw2Hw4HCwn144om/IyYmFrfc8gNhWUZablwQMqP88ca+eizLjoZiCFP3iIhGw6dlRlgdLiyZ4P3LxhzHttZ7TIoPwsXpEXh5zzFckRXF6d9ERMOk1WzF2gNNWDIhCtE+9m/ruVwnBAbqsXbth7xO8EC3TkvAByVNeHxrNZ68NntIy+sQuSMW2um8vVfShC6LA9+fnig6yoj59a9/g8ceexjXXbcUCoUCs2bNxr33/gIAoNFoEBl5ciEkICAQCoXilMdLSoqwe/dOPPvsyyc9/sADD+Lhh3+LZ599CjfeeAvS0saN7AF9y4nrxkmShPj4BFxyyeVYufIGaDTeOx1RkiTcMDkeD35Sjq9qOjArJVR0JCIiAMDaA81Ii/BDZpR33sA+Hba13uXeucnYVt2Of31ZjUeuHC86DhGRV3h1Tz2cLhm3+thoduDcrhOCgw28TvBQ/loVbp85Bn/bUoWvajtwUTL76OSZJHmIuyq0tvaM2vYLwcEGr1+D6kwMe/4JnU4NU7a4O6lnY3W4sPS53UgOM+Cp63JG5DN8/XsA8BwAI3cOHM6B7/CYUAP+M0Lf4eHE74LvnIOIiAAhwzeOt/O+cp7PRFQ7XN7Sg5teK8QvF6RiRe7p1xkdbfw+DOB5GDDU8/DsV0fx3x1H8fSKHExOCB6FZKOH34UBPA8DzvU8jFQbP5p99bPxxu+G6P55e68NS5/bjUvGReC3i4avCOyNvysek2f4rmOyO1247sW90KkVeP2myVAqPGtUuy/9rjzZhRzTUNpx31j8k4bduoPNaO+14fteujY7eT+VUoGVuXHYU9eJCiPXgSMi8dYeaIZWpcCizEjRUYguyE1T4hETqMXftlTB4XKb+h8RkUd6fW897E4XbvPimeREAKBWKnDP7GRUtfXh49IW0XGIzgsL7XTOHE4XXt1zDNkxAZjiZaOUyLcsy4mGXq3A6v0NoqMQkY+z2J34tNyIBWnhCNSpRcchuiA6tRL3zU3BkdZefFDSJDoOEZHH6uiz4e2iRlyaEYnEEL3oOEQj7uL0cEyIDsAzBbWw2J2i4xCdMxba6Zx9eKgFTd1WfH9GIjeoII8WqFPjqqxobCgzos1sFR2HiHzYZ4dbYbY6sTQ7WnQUomExPy0cUxKC8HRBLbr67aLjEBF5pNX7GmB1uLx6XzSiE0mShHvnpsBotuH1ffWi4xCdMxba6ZxYHS4899VRZMUEYBY3pyAvsCovDk6XjDWFjaKjEJGPkmUZ7xQ1IjnMgLz4INFxiIaFJEm4f/5YmK0OPFVQKzoOEZHH6eq34+2iRixMj0BymEF0HKJRkxsfhPlp4Xh59zG0ckAceRgW2umcvFfSBKPZhrtnJXE0O3mF+GA9FqSH453iRpitDtFxiMgHHWruQVmLGddNimXbSl5lbIQfVuTG4b3iJhxo7BYdh4jIo7y6tx59Nid+MIOj2cn3/HROMhwuGU9urxUdheicsNBOQ9Zvd+KlXXWYkhCEaWNCRMchGja3TkuA2erEO0Uc1U5Eo++twkb4aZRYPJ6boJL3uXPWGET4a/DIxiNwOF2i4xAReYS2XhvW7G/ApRkRGBvhJzoO0aiLD9bj+rx4fHyoBaXNPaLjEA0ZC+00ZGv2N8DUZ8dds5JERyEaVhlRAZiZFILV+xq44QoRjSpTnw0bK1qxZHwU/DQq0XGIhp2fRoVfLRyLI629eIObjxMRDclLu+pgd7rww4uSREchEua26QkINajx9y1VkGVZdByiIWGhnYbEbHXg1b31mJUciolxXD+WvM9t0xPR0W/H2gPNoqMQkQ9Ze6AZdqeM6ybFio5CNGLmjg3HvLFheGbHUTR2WUTHISJya83dFrxX0oQrsqKRGKIXHYdIGH+tCj/KT0JxYzc+P9wqOg7RkLDQTkPy+t56dFscuGvWGNFRiEZEbnwQJsUF4tW99bBzajsRjQKHS8a7xU2YmhiMJG5yRl7u/vmpUEoSHttUyVFpRERn8NxXdQCA27k2OxGumBCN9Ag/PLG1hrPPySOw0E5n1dlnx+p9DViQFo6MqADRcYhGzK3TE9HSY8X6MqPoKETkA7ZVtaOlx4oVHM1OPiA6UIe78pNQUGPCpoo20XGIiNzSUVMfPjrUjGsmxiI6UCc6DpFwSoWEn89PRXOPFav3cQk6cn8stNNZvbi7Dv12J+7kaHbychclhSA9wg8v7z4Gp4uj7YhoZL1d1IioAC3yU8NERyEaFSsmxSIzyh9/3VKFrn676DhERG7nvzuOQqNS4NZpCaKjELmNyQnBWJAWjpd216HVbBUdh+iMWGinM6rv7MdbhY24YkIUUsK42zl5N0mScNv0RNR19GPLEY62I6KRU9Pehz11nbhmYgxUCkl0HKJRoVRI+L9L09HZb8fftlSJjkNE5FYqjGZ8drgVq/LiEOanER2HyK38ZE4yHC4ZT26vFR2F6IxYaKczemJrDdRKCXfnJ4mOQjQq5qeFIzFEjxd21cHFNWSJaIS8XdQItVLCsuxo0VGIRtW4SH/8YHoi1pcZ8QVvahMRDfrP9loEaFX43pR40VGI3E58sB7X58Xj40MtKG3uER2H6Dux0E7fqai+C5uPtOGmqQmI8NeKjkM0KpQKCd+fnogjrb1cQ5aIRkRHnw3rDjZjUUYkQgwcsUa+57bpCUiP8MMjG4+gs49LyBAR7TragYIaE26bnoBAnVp0HCK3dNv0BIQa1PjblipurE5ui4V2Oi2XLOMfX1Yj0l/DO+rkcxZlRiIlzICnC2rhcLpExyEiL/NWYSOsDhdumsr1V8k3qZQKPHT5OHRbHPjL5krRcYiIhHK6ZDz+ZTViA7VYkRsnOg6R2/LXqnBPfjJKGruxvswoOg7RabHQTqe1odyI0uYe/Cg/GXq1UnQcolGlVEj4UX4S6jr68eGhFtFxiMiL9NudeLuoEXNTw5AcZhAdh0iYtAh/3D4zEZ8dbsXmilbRcYiIhPmktAVHWntxz+xkaFUs0RCdyRVZUZgQHYB/ba2B2eoQHYfoFPxXnE5hsTvx5LZaZET64/LxkaLjEAkxJzUM2TEBeO6ro7DYnaLjEJGXWHugGV0WB26aytliRLdMTUBmlD8e3VgJU59NdBwiolFnsTvxVEEtJkQH4JJxEaLjELk9hSThlwvHwtRrw/M760THIToFC+10ijf2N6Clx4r75qVAIUmi4xAJIUkS7pmdDKPZhreLGkXHISIv4HC68PreekyKC8TEuCDRcYiEUykV+O2icei1OfCHDRVcb5WIfM7r++rRarbhvrkpkNj3JhqSCdEBuCo7Gm/sb0BNe5/oOEQnYaGdTtLcbcGLu+owNzUMkxOCRcchEmpyQjBmJIXg5d3HOC2NiC7YZ4db0dxjxc1cm51oUGq4H+6dm4Lt1SasKeSNbSLyHW29Nry8+xjmp4VjUjxvwBOdi3vyk2BQK/HXzZW8UU9uhYV2OsnftlTBJQM/n58qOgqRW7gnPwldFgde21svOgoReTBZlvHqnnqkhBkwKyVUdBwit3LdpFjMTgnFv7ZW47DRLDoOEdGoeHbHUdicMn48O1l0FCKPE2LQ4K5ZY7C7rhNbjrSJjkM0iIV2GrS9uh1fVLbjBzMSERukEx2HyC1kRAXg4vQIrN5Xj/Zerh9LROdnR20HKtt6cdPUeC7LRvQtkiThN5eNQ7Bejf/7qAz93BuFiLzc4RYzPjjQhGsnxiAxRC86DpFHunpiLMaG++EfX1RzXzVyGyy0E4CBTVj+sqkSyaEGfG8KN2gjOtFds8bA5pTxVEGt6ChE5KFe2X0Mkf4aXJbBTcaJTifYoMbvL89AXUc//ra5SnQcIqIR45Jl/HlTJYJ0atx5UZLoOEQeS6WQ8MuFqWjuseI5boxKboKFdgIAPL+zDo3dVjxw8ViolfxaEJ1oTKgBK3Njse5AM8paekTHISIPs+9YJ/bXd+HGKfFsY4nOYEpiMG6dnoC1B5vxWblRdBwiohHx8aEWHGjqxk/mJCNApxIdh8ij5cUHY8mEKLy2tx6Vbb2i4xCx0E5ATXsfXttbjyXjI7kBKtF3uGPmGATr1fjb5iputkJEQybLMp4pqEWEvwZX58SIjkPk9n44cwyyYwLx8GcV7DATkdfpttjxxNYaZMcEYsmEKNFxiLzCfXNS4K9R4tHPj8DFvjoJxkK7j5NlGY9uPAKDRomfzk0RHYfIbflrVfhRfhKKG7uxvoyj7IhoaHYf7URhQzdunZYInVopOg6R21MpFfjzVZkwaFT45dpD6LbYRUciIho2zxQcRZfFjgcWjuWeLUTDJNigxk/npqC4sRvrDjSLjkM+joV2H7f2QDP213fhntnJCDVoRMchcmtXZkVjfHQAHv+ymh1/IjorWZbx9I5aRAVosSw7WnQcIo8R4a/Fn6/MRHO3Ff/v43I4XRydRkSe77DRjHeKG3HNxFiMi/IXHYfIq1w5IQq58UF4YlsNTH020XHIh7HQ7sOaui3455fVmJIQxAIA0RAoFRL+9+I0dPbb8e94BozYAAAgAElEQVRtNaLjEJGbK6gx4WBTD34wIxEaFS+5iM7FxLgg/HJBKr6q7cAzO2pFxyEiuiAuWcZjX2+AetesMaLjEHkdSZLwPxenoc/mxONfVouOQz6MvT4f5ZJl/H5DBWQZePCycZy2RjRE46L8sSovDu+XNKO4oUt0HCJyU7Is4+mCo4gL0uFKrsFKdF6unhiLZdnReHHXMWyuaBUdh4jovK090IySxm78eHYyAnVq0XGIvFJymAE3T43HJ6VG7KnrEB2HfBQL7T7qnaIm7K3rxL3zUhAbpBMdh8ij3HlREqIDtHj4swpY7E7RcYjIDW2pbMdhoxl3zBwDlZKXW0Tn65cLxiI7JhC/XX8Yh5q6RcchIjpnxh4rHv+yGv+/vfuOr6q+/zj+urnZexMggxUOYS+BiiAOwFW1rtaBq3WP+rO1rdW22tbaWrVOHG3VurHFunCgKCpaFdnzMEIYgYQkZO/ce35/nARDRMgl49zcvJ+PRx433Jx7+Xy/Z3y+53u+53smZMRx2khdfBfpSpdNziQ9Ppw/vb9Z5+riCJ359UK7ymp5+JNcpgxI4AeaMkbEZ5Ghbm6fNZS8fbU89lme0+GIiJ/xWhZPfp5HVkIEJ+WkOh2OSI8WGhzEPWcMJzEqlJv+u47t+2qcDklEpN0sy+LPH2ymyWtx+6yhupNcpIuFh9jn6rvK6nSuLo5QR3sv47Usfv+uSbDbxe2zhuJSohc5IpMHJHD2mL68tCyf5bvKnA5HRPzIexv3srW4hiuPzsIdpDwr0lHJUaE8fPYoXMAN89dQVFXvdEgiIu2ycGMRn+bu45qpA0iPj3A6HJFeYUJG/P5z9dW7dTecdC91tPcyLy7LZ0V+BTfPGEyfmDCnwxHp0W6cbk+9dOc7JpV1TU6HIyJ+oK7Rw6Of5jEsNZoTjRSnwxEJGJkJETxw1kjKahv56atrqapX3hUR/1Za08C9H21lZN8YfjS+v9PhiPQqN0wfSJ+YMP7wnkl9k9fpcKQXUUd7L7J2TwWPfLqNGUOSOE0PZhPpsMhQN78/ZRiFlfX86f1NWJbldEgi4rCXludTWFnPTTMG6fZwkU42PC2Gv54+gm0lNfzstXU6cRYRv3bvh1upqm/i9llDdYebSDeLCg3mtlnZ5O2r5e//2+50ONKLqKO9l6ioa+TXb20gNTqU38zWlDEinWV0v1iunjqADzYV89qaAqfDEREHFVc38MyXO5kxJIkJGfFOhyMSkCYPSOCOkwyW7yrnltfV2S4i/unjLSUsNIv48ZRMBidHOR2OSK80ZUAip4/sw/NLd7K+oNLpcKSXUEd7L2BZFn94bxN7qxr402k5xIaHOB2SSEC5eFIGkzLjue+jrZiFVU6HIyIOefyzPBo8Xm6YPsjpUEQC2uycVG6bmc3/8kr5uTrbRcTPFFXV88eFm8hOieKSSRlOhyPSq9107GASo0K5811NISPdQx3tvcC8FbtZvKWEG6YNZGTfWKfDEQk4QS4Xvz9lGHHhwdzyxjrKahqdDklEutmmvVW8saaA88b1IzNBDzsT6Wpnju7Lb2YN5cu8Um6cv0bPShERv+DxWvz2HZO6Rg9/OjWHELe6XEScFBMezG2zhpJbUsPDn+Q6HY70AjrqB7j1BZU8+HEu0wYlcsEEPYBFpKskRYVyz+nDKa5u4LYFG2jyar52kd7Csiwe+DiX2PBgfjwl0+lwRHqN00el8YdThrF6dwU/eXklBRV1TockIr3cs0t38vWOMn5+/GAGJEU6HY6IAFMHJvKj8f2Zt2I3S3JLnA5HApw62gNYWW0jt765nqSoUH53kqF52UW62Ii+sfzqhGy+2lHGvR9u0cNRRXqJz7btY+mOMn7yvSxNzybSzWbnpPLw2aMorKzn8pdWsmmvpnATEWesyi/nic/ymGmkcPrINKfDEZFWrp82kOyUKO58dxPFVfVOhyMBTB3tAarJ4+XWN9dTXN3An7+fQ1yETvxFusPpo9KYMzGd+av28MKyfKfDEZEuVtfo4f6PtpKZEME5Y/o6HY5IrzQxM55//GgsLuDKeav4cnup0yGJSC9TWdfEb97eSJ/YcH49M1uD3ET8TFhwEHedmkNto4c73jXxalCcdBF1tAeovy3O5eud5fx65lDNyy7Sza6fPpAThibz0Me5vLthr9PhiEgXevqrnewsq+OXJwwhWPOwijhmSEoU/zx/LH1iwrhx/hqe/nKHTqJFpFtYlsVd729ib1UDd506jOiwYKdDEpGDGJgUyc3HDebL7WW8qEFx0kV0RhiAXly2i1dW7uaCCf05dUQfp8MR6XWCXC7uOMlgfEYcv3tnIws3qrNdJBDlllTz7Fc7OWV4KpOyEpwOR6TXS4sN55/nj+WEoSnMXZLHTa+u1QPKRaTLPbd0F4s2FXPt1AEa5Cbi534wKo3jspN59NNtrNtT4XQ4EoDU0R5gFm7cy98W53JcdjI3Th/kdDgivVZ4iJv7zxzJmH6x/PbtjXy4qcjpkESkE3kti7vf30xUqJubjlW+FfEX0WHB3HXqMH55whC+3lnGhc8tY1V+udNhiUiA+nzbPh75dBsnDk1hzlHpTocjIofhcrm4bWY2qdGh/OINe7plkc6kjvYAsnRHKb97x2Rcehx/OGUY7iDNCyfipMhQN387ayQj+sby6wUb+XhLsdMhiUgneXNtASvzK7hx+iASIkOdDkdEWnG5XJwzth9PnT+WEHcQV81bxWNLttHQ5HU6NBEJIHklNdy+YCNDUqL47UlDNS+7SA8RFxHCX88YQXldE7e+uZ5Gj9oH0nnU0R4gzL1V3PL6erISI7jvjBGEBWvViviDqNBgHjxrJDl9ovnVmxvU2S4SAPbVNPDQJ9sYlx7H90dqijYRfzWsTwzPzxnPSTmpPPXlTi56fjlrdZu4iHSCfTUN/PS/awlxu7j3jBFEhLidDklEfDA0NZrfzh7KyvwK7vtoq9PhSABRb2wA2FVWy09fXUt0WDAPnjWKmHA9fEXEn0SHBfPw2aMwUqP5xRvreXX1HqdDEpEOeGBxLjUNHm49MVuj10T8XHRYMHecPIwHzhpJdX0TP35pJQ8szqWu0eN0aCLSQ9U1evjZa+soqW7g/jNH0C8u3OmQROQIzBqWysVHZTB/1R7+q3N06STqaO/h8strueaV1TR6vDx09kj6xIQ5HZKIHER0WDBzzx3NlAEJ3P3+Zh77LA/LspwOS0R8tHhzMe9s2MslkzIYmBTpdDgi0k5TByYy79KJnDmqLy8s28UPn/maxZuLlYtFxCcNTV5+8cZ61u2p5I+nDGOEHn4q0qNde8wApgxI4J5FW/RMF+kU6mjvwfLLa7l63mpqGj3MPWc0g5KinA5JRA4hMtTNfWeO5IyRaTz1xQ7ufG8TTZoPTqTHKK6q548LNzEsNZofT8l0OhwR8VF0WDC3zszm8fNGExHq5pY31nPjq2vJ21fjdGgi0gM0eS1uW7CB/+WVcvusoczITnY6JBHpIHeQi7tOHUbf2DB+/vp6dpbWOh2S9HDqaO+hckuqufLlVdQ0enj0nFEYfaKdDklE2iE4yMVts7K58ugsFqwr5KevrqW8ttHpsETkMLyWxZ3vbaKuycsfThlGiFtNKJGeakJGPM/PmcDPjhvMmt0VnP+vZTz8SS7VDU1OhyYifsprwR3vbGTxlhJ+dtxgTh+V5nRIItJJYsNDeOCsUViWxY2vrmFfTYPTIUkPprPEHmhdQSVXvryKJq/F4+eNZlifGKdDEhEfuFwurvheFr+dPZTlu8q5+IUVmHurnA5LRA7hlRW7+SKvlJuOHcQATRkj0uMFB7n40fj+zL/8KE7OSeXZpbs49+mveW/DXk0nIyIHsLD4yNzLexuLuPaYAfxofH+nQxKRTpaZEMHffjCSoqoGbnp1LVX1uvguR0Yd7T3Mx1uKuXreKqJC3fzjR2PJTtFIdpGe6vsj0/j7j8bQ5PHy45dWsmBdodMhichBbCmu5uFPcjlmUCJnj+nrdDgi0omSokL57UkGT50/luSoUG5/eyNXv7KaLcXVTocmIn7Aa1l8llvKmvxyLpucwWWTNXWcSKAa1S+Wu0/LYVNRNTf/d60enC5HRB3tPYRlWbzw9S5ueX09g5Kj+OcF48hIiHA6LBHpoJF9Y3luznhG9o3hjndN7lm0hUbN2y7iNxqavPz27Y1EhQZz+6yhuFwup0MSkS4wql8sT18wjltnZrO1uJqLnl3G/R9t1Yg2kV6syWvxh/c2sXZPBeMzE7hm6gCnQxKRLjZtcBK/P9lgZX4FP399nTrbxWfqaO8Baho83LZgIw98nMuM7GSeOG80yVGhToclIp0kMTKUR84ZzYUT0vn3yt1c/uJKPZhNxE888HEum4uq+c3soSQp94oENHeQi7NG9+U/lx/FGaP68vLyfM5+ailvry/UdDIivUxdo4db31zPW+sKmZgZz7TsZF1sF+klZg1L5fbZQ/lqexk3zl+ji+7iE3W0+7ltJTVc+sIKFm2y54P78/dzCA9x7/97XV0d9977Z84993Rmzz6Wq666jKVLvzjkdy5a9D6nnXYi119/ZVeHLxKQdu/O5/rrr+SYYyayZ8/uQy47b94LXHDB2Zx44jGcddap3Hvv3VRWVn5rueAgFzfNGMS9ZwxnT0Udc55bzmur9+jEXsRB72wo5N8rd3PhhHSO6h+lfCvSjboi17ZXfEQIt87M5pkLx9EvLpzfvWNyxcur2KTnqYj0CiXVDVz9ymo+3lLCzccNZmJGPIfqYtc5uYgzfGkrWJbF/PnzmDlzGnfddcdhv/v0kWn88dRhrN5TybX/Xk1ZTWMnRS2BTh3tfmzhxr1c8sJyymobeeScUVw2OZOgNlfR77//L6xdu5r77nuYN95YyMknn8Yvf3kzO3bkHfQ777jjNp599ikyMjS3nMiR+Pjjj7jqqstISzv8PM1vvfUaTz45l5///Fbee+9jHnzwMVauXMGDD977nZ85dkgyL10ygVH9Yrnr/c386s0NlNcqqYt0t+Kqeu5auJlx6XFcP32g8q1IN+rqXNtew9Ni+Of5Y/nNrKFsL61lzvPL+f1b66ms08g2kUCVW1LN5S+uYEtxNfecPpzz2/HgU7URRLqfL22FhoYGfvrTa1i8+ENSU/u0+/+YNSyVe88YTm5JDVe+soq9lfUdCVl6CXW0+6EGj5f3NxRy24KNZKdE8/yc8RyVmfCt5SoqKli48B0uv/xKMjOzCAsL48wzzyYrawCvvTb/oN/dv386f//7v+jbV09KFzkSlZXlPPro35k9+5TDLrtx4wYGDRrC+PETcbvdZGRkMnXqNDZsWHfIz6VEh/HIOaO4cfpAPtlawgXPLuPLbSWdVQQROYzaRg9vrN5DTFgwfzoth5qqSuVbkW7UHbm2vYJcLk4flcb8yydy9ph+vPDVDs55eimLNhXprjORAPPV9lJ+/NJK6pq8PPHDMczITj7sZ3ROLuIMX9oK9fX1TJo0hQcffIzY2Dif/p9jBiXx4FkjKayo54p5qzTFqxyWOtr9zLKdZfx75W7W76ngkkkZPH7eaFJjwg66rGluoKmpieHDRxzwfk7OCNatW3vQz1xxxTWEhmqOWZEjddppZ5KZmdWuZadPP45t27aydOkXNDU1sXt3Pp9//inHHz/zsJ8NcrmYc1QGT10wlvAQN3OeXsrDn2yjoUkPShXpSg1NXhZu3EtNfRP3njmC5KhQ5VuRbtZdudYXseEh/OKEIbx69dGkRofxqzc3cMvr6zW6TSQAWJbFS8vzufHVtaRGh/HMheMYkRbTrs+qjSDiDF/aCjExMVx00aUEBR1ZF+iEjHjmnjeamgYPl76wgiW5GgQn3y3Y6QDEVtfoYe6SPF5ans/t0S7Om5BO2DEDD/mZsrJSAGJiYg94Py4untLSfV0Wq4i0z6RJU7juupu45Zab8Hg8WJbFCSfM5LLLrmj3d+T0ieH5OeN55LPtPLt0J0tyS/jdSQbD29n4F5H2syyLP72/iUEV9ZwyMo3k5v1M+VbEf3VGrvXFiH6xPH3hOF5atosnPt/Oec98zY3TB3Lm6L7fmuJRRPxfdUMTf3xvMx9sKmL64CTuPNkgOqz93SRqI4j0DiPSYnj2onHc8vp6bv7vOq6amnXQ6Z1FNKLdD3yZV8r5zy7jpeX5nDe2H+eM7UvfuIgOfaeeiC7ivEWLFvLkk3P5y1/+xgcfLOG5515h165d/PnPf/DpeyJC3Nx15kge+MFIKuubuPzFFTz2WR6NHo1uF+lMc5fksWD9Xo7KjGdon/ZdzFK+FXFWZ+VaXwQH2XedvXzJBIanxXD3B1u4WreTi/Q420pquOyFlXy4uYjrpw3kr2cM96mT/XDURhAJLH1jw/nHj8YwOyeVxz/bzq/e3EB1g57bIgdSR7uDiqsbuH3BBq6fv4Ygl4vHzh3NLScMIaSdt7MkJiYBUFFRfsD75eVl+/8mIs6ZN+9FTjhhFpMnf4+wsDAGDhzExRdfxjvvvEVNTbXP3zd1UCIvXzKBk4b34akvdnDx8yvYWFjZBZGL9D7zlufzzFc7OWt0X8ZnHDh3o/KtiP/q7Fzri/T4CB49ZxS/mT2UrSU1XPjsMp7+cgdNuhAu4tcsy+Lt9YVc8sJyyusaefSc0VwyKeOIRqaqjSDSu4SHuPn9yQY3HTuIj7cUc8nzKzALq5wOS/yIOtod4PFa/Gflbs59eikfbi7myu9l8eLFE5iYGe/T9xhGDqGhoaxbt+aA99esWcWYMeM6M2QROQJerxev13PAe01N9r+P9AFqseEh3HGSwf1njqCstpFLX1jB4xrdLtIhb6wp4N6PtnLs4CR+ccIQXBx4oq18K+K/uiLX+sLlcnH6yDReuXQi0wcnMXdJHpe8oJNuEX9VUdfIbQs28rt3TIzUaJ67aLzP5+GtqY0g0vu4XC4unJjOo+eMpqbRw2UvreC5pTt1oV0AdbR3u2U7y5jz/HL+smgLw1KjefHiCVxxdBZhwb6viujoaE455XT++c8n2LFjO3V1dbz44nMUFOzhzDPPpqhoLxdccDZr167ugpKISFvr16/lggvOpqCgAIBjjz2eDz98n+XLv6apqYn8/F28/PJzTJlyNFFR0R36v6YNTmLepROYnZPKP7/YwYXPLWdVfvnhPygiB3h7fSF/XLiJKVkJ3HVaDu6gb49mU74V8R/dmWt9kRQVyt3fH849pw+npKaRS15YziOfbqNeDzEX8RtfbS/l/H8t48PNxVx7zAAeP28MqTFhHfpOtRFE/E/btkJXmZgZz4sXT2DqwEQe+mQb5z75hS60ix6G2l32VNTx0Me5fLCpmLSYMO4+LYcThiZ3eN62G2+8mblzH+Laa39CTU0N2dlDue++h0lL68uePbvZsWM7tbW1AKxcuZybb74egKamJizL4vjjjwbg/vsfYezY8R0rpEgvcP75Z1FYWIDXa584X3DB2bhcLmbPPoWZM09ix47tNDU1Ni97EQD33fdnCgr2EB4ezvTpx3P11dd1Siyx4SHcefIwZhop/OWDLfzk5VWcPaYv1x0zkJhwHd5FDueNNQXc9f4mJmTG89czhh/yorfyrUj38adc66vjspOZkBHHA4tz+ddXO/loczG/mTWUselxh/+wiHSJ2kYPjy3J46Xl+WQlRPD0BSPIaeezWNpDbQSR7udLW+Hddxdwzz13AdDY2Mi6dWtYtGghAC++OJ+0tL5HHEd8RAj3nD6cDzYVc//irVzywnIumJDOlUdnER7i7mAppSdytfeWyqKiyq6/97JZfHwkZWWB8TCh2kYPz361k+e+3gXAJZMymDMx/ZA7XOTSBwgPD2HfKGdOEPxFIG0HR0p1oDpocbh6qGnw8MTneby8PJ/EyFBuOX4wx2V3/GKeP+kt20JKSowjK60lz/eWen5x2S7+tjiXKVkJ3HPGcCJa5WXl4W/0lu3hcFQPNtWDb3XwZV4pf3p/E7sr6jl3bD+umzaAqNDAuBCubcHmaz10VY7vznP1w/G3beOLvH3c/f7m/fvhjdMH+tz5FajtAn9bV51BZeoZArFMAK6wEP745jpeW1NAv9gwrps2kBONlCN6/oO/CMR11ZEytSePB0ZLzw95vBbvbtjL3CXb2FvVwOxhKVw/bSBpseFOhyYiASgy1M3/zRjMSTmp3LVwM798cwPTBiXyixOG6Lgj0orHa/HIp9t4/utdHJ+dzB9OGUboEUzfJiJyOJMHJPDSJROZu2Qbr6zYzadbS7h1ZjZHD0x0OjSRgFdW28gDi7eyYP1eshIiePKHYxinO0tEpAvFRYRw26yhnDw8lb8u2sptCzby3NJdXDdtAJOzEgJqEJx8N3W0dzLLsvh4SwmPfZZHbkkNOX2iuevUHN0uKiLdIqdPDM9cOI6Xl+fzxGd5nPfM11w2OZMLJqQf0bMgRAJJbaOH3769kcVbSjh3bD9uPm4wwQeZk11EpLNEhrr5+fFDmGmk8MeFm/jpq2s5PjuZ/5sxSBfCRbqA17J4a20hj3y6jYr6Ji6fksnlkzPVDhaRbjM+PZ7n54znvY17efyzPG6Yv5aJmfFc9b0sxvSPVYd7gFNHeydauqOUuUvyWLunksyECO4+LYfjhyb36NtERKTnCQ5ycdHEdI7PTuaBj3OZuySP19cU8H8zBjF9cJISu/RKeftq+OUb68nbV8PPjxvMD8f3dzokEelFxvSP44U5E3j+61089eUOPt+2j8unZHLhhHTdVSPSSdbsruCvH25hQ2EVo/vFcuuJ2QxJiXI6LBHphdxBLk4Z3ocTh6Ywf/UenvpiB1fMW8WItBgumpjOjOxkDfgJUOpo7wTrCiqZ++k2vtpRRmp0KLfPyubUEWnaaUTEUf3iwrnn9OF8tb2U+z7ays9fX8/krHhumD4IIzXa6fBEus17G/byp/c3ExocxENnj2JyVoLTIYlILxQaHMTlUzI5eXgq93+0lblL8nhrXSHXTRvIcUN0IVzkSBVV1fPokjwWrCskJTqUP5wyjNnDUrRPiYjjQoODOH98f84clcZb6wp5adkubn1rA/3iwvnhuH6cnJNKQmSo02FKJ1JH+xGyLIulO8r411c7+WpHGXHhwfzfjEGcPaafbksTEb8yKSuBFy6ewPyVu3nyf9u56LnlzDJSuGrqADITIpwOT6TLVNQ1cs+iLby3sYhRfWO5+/s59IkJczosEenl+saG89czRvC/vH3c/9FWfvnGekakxXDtMQOYpAuBIu1WXtvIs0t3Mm/FbryWxSWTMrh8ciaRob497FREpKtFhLg5d2w/zhrdl0+2lvD817v42+JcHv5kG8cMSuS0EWlMHZhAsFv9iT2dOtp95PFaLN5SzL++2smGwiqSokK5YdpAzhrTl+gwVaeI+KfgIBc/HN+fU4b34fmvd/LisnwWbSri9FFpXD45U/PESkCxLIsPNxdz74dbKa1t5OqpWVwyKVN3momIX/negEReuiSBt9cV8uT/tnPdf9ZwVGY8Vx2dxeh+msNV5LvUNnp4eXk+zy7dSXW9h5NyUrny6CzS4zWARET8mzvIxXHZyRyXncyWomreWlfIOxsKWbylhMTIEI4dksSMIckclRlPiDrdeyT1DLdTcXUDb6wp4NXVeyisrCcjPpxfz8zmlOF9NIJdRHqMmPBgrjlmIOeN68/TX+5g/qo9vLG2kJOGpTDnqAwGJ2seS+nZ8vbV8MDiXD7btg8jNZr7fzCCnD4xToclInJQwUEuTh+VxuycVOav2s3TX+7kJy+vYmTfGC6YkM5xmsNVZL+y2kb+s3I381bspqy2kemDk7hm6gDNwy4iPdKQlChumjGI66cN4PO8Ut5ZX8i7G/by39UFRIe5mTowkamDEpmYEU9KtO7K7SnU0X4IHq/Fsp1lvLamgA83F+PxWkzKjOdnxw1m+uAk3Gr0ikgPlRQVys+PH8JFE9N5YVk+r63ew4L1ezlmUCIXTUxnfHqcRtJJj1Jc3cAzX+7gP6v2EB4cxE3HDuKH4/urg0pEeoSw4CAumJDOD0b35c21hby0fBe/fmsDfWPDOHesPYdrsk6ypZfaXV7Hi8t28fqaAuqavBwzKJHLJmcyul+s06GJiHRYsDuI6YOTmD44ifomL19tL2XxlmI+2bqP9zYWATAgMYKJGfEclRnP+Ix44iNCHI5avos62tuwLIsNhVW8t3EvCzcWUVzdQExYMD8cZ8+llJUY6XSIIiKdJi02nJ8dN5gfT8nk3yt3M295Ple/spqshAjOGJXGqSP6kKiHs4gfK6io46Xl+cxftYdGj5czR/XlqqlZ2m5FpEeKCHFz3rh+nD2mL59uLeGFZbt46JNtPPLpNo7KjOeknFRmDEnWlJUS8Dxeiy/ySnl19R6W5Jbgcrk4KSeVORPTdQemiASssOAgpg1OYtrgJDxei81FVSzdUcbXO8tYsL6Q/6zagwt7NPyItBhGpMUwPC2GQclRGmDkJ9RCAxo9Xlbml7Mkdx+fbi1hZ1kdIW4XUwcmMntYKscMSiQ8RA9UEZHAFR8RwhXfy2LOxHTeN4t4fU0BD32yjUeX5DF9cBIzjRSOHphAVKjShjjPsiy+2lHGv1fs5tPcEgBOzknl8ilZesCviAQEd5CLGdnJzMhOZltJDe9u3Mu7G/Zy57ub+HPwFsanxzFlQAKTsxIYlBSpu9AkYOypqGPBukJeX1NAQWU9iZEhzDkqg3PH9tMDzUWkV3EHuRjWJ4ZhfWKYc1QGTR4v6woqWbqjjBW7ylm0qZjX1hQAdge9kRrNiLQYjNRohqREMTAxklBNdd3temWPidey2FZSw8r8cr7eUcb/8kqpbvAQ4nYxIT2ei4/K4PihycSG61YMEeldwkPcfH9kGt8fmca2khpeX1PAOxsK+WhzMSFuF5MyEzh2SBLfG5CgB6hKt9tVVsuHm4p5Y2ZK9BsAABgXSURBVG0B20triY8I4eKjMjh7TF9tjyISsAYmRXLN1AFcfXQWq3dX8L5ZxJfbS/nb4lwAUqJDGZ8eR06fGHLSojFSo3VhXHqU/PJaFpnFLNpczPqCSgAmZ8Vz04xBTB+cpAcCiohgTzEzpn8cY/rHAfbgo51ldawvqGR9QSXrCip5dfUe6pu8ALhdkJUYSXZKFEOSoxjS/NonJkwX6LtQr2iB7atpwNxbxaa91azdU8GKXeWU1zUBdsP0RCOFaYMSOSozgcjQwBq5Pnfuw/z1r3dTXV3ldCgivUZUVDS33HIr1157g9OhdMjApEhumjGIG6YPZM3uCj7aUsziLSV89v4+APrFhTMuPY7x6XGM6RdLRkIEQUrY0oksyyK3pIaPt5SwaFMRm4qqARjVN4Y7TzY4YWiK3zyQXPlWpHsFSq71hcvlOuAEu6Ciji+3l/JFXhkr8yv2z+PqAjISIshs/kmPjyAzPoI+MWEkR4cSFerWCbY4qq7Rw8r8cr7aXsaX20v35/ecPtHcMG0gJxjJ9I8LnDvU1EYQcU4gtxdcLtf+XH9STioATV6LnaW1bC6qYmtxNZuLqlm9+5s2AkBMWDADEiPITIxkQEIEWYmRZCVGkBEfoQubncBlWVa7Fiwqqmzfgp0gPj6SsrIanz7T5PGyt6qBnaW1bC+tZWdZLdv31bC5qJri6ob9y6XHhzO2f9z+zqH+ceF+19CMXPoA4eEh7Bt1XYe/a9SooRQWFnRCVCLiiz590lizZlOnfd+RHBe7gmVZbC2uYelO+3a1FbvKKattBCAyxE12ShRDU6PJTonaf3KfEh3aKR3w/lIHXS0lJcaRpNSS552s5/omL7kl1fu3rZX5Ffu3r9H9YjlhaDLHZSfTt4tHrx9JHla+Fel+nZ1r28Ofc1FJdQMbC6tYX1jJ5qJqdjafE7WMbGsRHhxEcnQoKVGhJEeHkRgZQkxYMDHhwcSEBRMbbv8eGxZCdJib2PAQIkKCDjhn8ud66E6+1kNX5fjuPFc/nLZ1YlkWBZX1bCisYkNBJWv3VLB6dwUNHovgIBdj+scydWAixw/13871jp6fq40g4qzuai/4c26srGtia3E1W5p/tu+rIW9f7QH9pW6XPZguKzGSzIQI+sWGk90/jvhgF/1iwwNmSu2OrKf25HFHR7R7vBZ1TR48XguvF5osC6/XohoXJaW11DQ0UdPooabB/qluft1X00hJdT0l1Y0UVzdQXN2w/0S8RURIEBnxEUzKimdoin0LZXZKFHG97Mm811xzg66ei3SzqKhorrkm8K6Yg33VfEiKfdvZ+eP7Y1kW2/bVsGZ3BZuLqjH3VvH2+kKqGzz7PxPithNzenwE/ePCSYu1R9QlR4WSHBVGclQo0WEaXdcbWJZFZX0TRVUNFFc1UFRdz66yOnJLasgtrmZnWS3e5q6C/nHhHDMokXHpcUzJSiDVz+dlVb4V6V6BnGuPVFJUKFMHJTJ1UOL+97yWRVFVA7vKatlbVU9xlX3uZB+D7bt+99U0UFXvOcQ32/PExrbqjE+KCSPC7SIuPIS4iGBiW7+GBxMXHrK/w153uwU+r2VRVttIcVUD5bsr2Zhfxo7mCz25xTWUNp+ru4NcDEmO4pyx/ZiclcC49DgiAqTj5lDURhBxjtoLtpjwYMamxzE2Pe6A96vqm9hRWkvevhq2l9oDlrfvq2XpjrJvXahPjAyhf1w4/Zp/0mLCSIkOIyU6lJToMBIiQ5TzcXhE+9WvrGLZznKfPxcc5CIpqqWTJpTk6FCSIkNJiQ7df5tkclRoj+206cwR7T2ZP18N7C6qA9VBi55UD17LYnd5HflldeSX15JfXseusrrm19oDOuFbhAUHkRQVSnyEfWIeF/7NyXpshP3aNymKoCYP4SFuIkLcRIQEERHiJjzEHVBPWA+UEe0FFXXc8vp6SmsbaWjy0uDxUtfkxeM9sDkR5IKM+AgGJUcxKCmSwclRjO4X6+gDz5SHv9GTjj1dSfVgUz0Ebh14vBbVDU1U1DVRWW+/VjW/Vja/V9nq3zVNXvZV11Nea7//XVxg5/Xm/B7buhO+ueM+tjnnx7b5t79MDXYogTyi/cNNRWworMLjtfBYFh6vRYPHe8AAuOoGDyXVDZTWNOBpE0F8RAiZCREMSIxofn5ADEOSo3rEem0rUNsFgXg8U5l6hkAsEwRWuSzLoqSmkUqPhZlfzu7yOvscv8J+Layo+9Zx3x3kIjkqlNRo+4651Gj7/L7lJy4i+Jvfw0Mce1BrQI9ov2xyJscMqibIZXeeB7lcuINcREeF0VjfSGSIm8hQN1GhbiJDg1v97tZVEhERPxXkcpEeb08bAwkH/M2yLKobPPtH07XclWT/Xk95nX0Sv6usdv/JfHvOHEPdrv2d7i0d8GHBQQS7gwgJchHiDiLE7SL4gN8PfA1xuwgJCiK4ebkgl4sglz2Kv/VrkMuFywXj0+Md7Qz2d+HBbnLSomn0WIQFBxEWHESoO4iEyBCSo0L3j35IjQ5zrJElIiI2d5DL7uwOb9/dv61PUj1ei8q6JsrrGqlo9VpWa79W1DVR3vx7aU0jeftq93feH0pYcBDRYcH783pky4X20G9y/f583ybXt87/9t/s99wucGHncVernO7im1zvAiJC3QxJjupotfZo81ftYfmuctxBLtzN5+khbtcB5+Yp0aEMS40mKSqEpKhQEiNDGdo/noRgFzHhveJxcCIiAcnlsjvNh8RHMjD22+e8TV6LfdUNFFXVs7fKfi2q+ubf20qq+Wp76UEH2bWIDHETGx7cnNfdRIYE7R9UFxniJjwkiMhQN6HuINxBdn5v/dqSm4LdLju3Q3N+dzEuPY7kqNAurKHv5mj2m5yVwOSshG+9H0hXgY5EY//vERbdtfPPiog4weVyER0WTHRYMAMSIw+7vMdr7R9R5wl2s6ekitpGL3WNHmobPdQ2eqlt9DT/+8Df65o8NDZ5qfFaNHm8NLa8eqwDfm/yemloezm+Hb4/og+/Pck4kmroFeIjQ/j1zKFOh3FElIdFRNrPHeQiPjKE+EjfpuhsyfGtR8qX1zUe8O/K+qYD8n1VQxNF1fXUNnioaX6v7a3tneWxc0czMTO+S767J3j03NFH9LlAPJdXu0BE5EDBQS5SY8JIjQljxCGWa/R4Ka9tpKz5ontZbWPzq53zy+uaqGueMryu0UNRVUNz3m/+afB8a+R8e5w5Ko3bZjlzLqrLzH6osd9krPhICLAGioiIr9xBLuIiQoiLCCE+PpIBMV1zVdqyLDwWrTrivViW/b7XsqfDsWh+tcBrQd+DXNmXwKA8LCLS9Vrn+I5oncObvBaN+y+kN//utfB47GlPWvJ465xuYed6LPA2/x7mDmJ8Rtzh/mvpJdQuEBE5MiHuIJKjw0iOPrJz55bzcY/Xzuue5p8myx4457Esmjz2uTrN+d3CIiPeuYdrq6NdRER6PZfLRbALgoPctPOueREREfEDrXO4iIiIBA6Xy4XbZV+cd2YiGN9pUlQRERERERERERERkQ5QR7uIiIiIiIiIiIiISAeoo11EREREREREREREpAPU0S4iIiIiIiIiIiIi0gHqaBcRERERERERERER6QB1tIuIiIiIiIiIiIiIdIA62kVEREREREREREREOkAd7SIiIiIiIiIiIiIiHaCOdhERERERERERERGRDlBHu4iIiIiIiIiIiIhIB6ijXURERERERERERESkIyzL8rufO+644w6nY3D6R3WgOlAdqA5UD6oD1bPqwekf1YPqQfWgOlA9qB5UJ4FZLpWpZ/yoTD3nJxDLpTL5/uOvI9p/53QAfkB1oDoA1QGoDlqoHlQH3UX1bFM92FQPNtWDTfWgOmiherCpHr4tUOskEMulMvUMKlPPEYjlUpl85K8d7SIiIiIiIiIiIiIiPYK/drTf6XQAfkB1oDoA1QGoDlqoHlQH3UX1bFM92FQPNtWDTfWgOmiherCpHr4tUOskEMulMvUMKlPPEYjlUpl85LIsqyu/X0REREREREREREQkoPnriHYRERERERERERERkR5BHe0iIiIiIiIiIiIiIh2gjnYRERERERERERERkQ4IdjoAwzDigbnAcdgd/x8A15qmWX6QZWcAHwH1bf50mWmaL3VxqJ3KMIwM7HJ/D6gFXgduNk2z4SDLngPcDgwGcoE7TdN8tRvD7RLtrQPDMC4Fnubb6/140zQ/74ZQu5RhGKOAl4Bo0zQHHGK5gNwOoH110Au2gyzgfmB681sfATeZprn7IMseC/wFGA7sBh4wTfPx7oq1q7S3DgIpFzitt+ZgUB5uoVxsUy62KR8rH7dQTrYZhjEFex2PA2qwy/p/pmkWHGTZgD4+gG/thublpwN3A6OAMuBl4NemaTY5eSzprDaAYRgu4A7gIiAJWA7cYJrmuq6M/7v4WK4fAL8FsoEC4AnTNP/a/Lc7mv/W9nODTdPM77ICHERntVP8aV35UKa/A3PafNwNLDFN8zh/Wk/QOW0pf1pPzfG0t0w9Yn9qjqfDbT1/W0/Q7nJ1yz7leEc78HcgFhgLWMCzwBPAj77rA6ZphndPaF3qVWAtMASIA/4L/B74VeuFDMMYDTyPXR/vArOAeYZhHGWa5tpujbjztasOmm0/1IGtpzIM4zzgb8BX2A3471ouYLeD9tZBs4DcDpq9CazGbnCEYyeJJ4HTWi9kGEZa87K/BJ7BrrN3DMPIM03z3e4MuAu0qw5aBEgucFpvzcGgPNxCuVi5GFA+bkX52Nbrc7JhGAnAQuA3wIlAAvAK8DhwZptlA/r40Eq72w2GYWQCbwO/BmYAw4D3gL3Avc2LOXUs6aw2wLXAZcCp2B2GvwIWGIYxzDTNum4qS2vtLdck7H36IuA17A7fdw3D2Gaa5n+aF/vENM0Z3RT3oXRWO8Wf1lW7ymSa5hXAFS3/bu7cXIK97lr4xXrqxLaU36wnH8rUY/anTmzr+c16gvaXq7v2KUenjjEMow9wFnCraZqFpmnuxb6ydY5hGMlOxtaVDMOYCIwHbjFNs8w0ze3An4ArDcNou06uBBaapvmaaZp1pmm+ASwCftK9UXcuH+sgkEVjH4gXHWa5gNwOmrW3DgJW8+igr4FfmKZZ0Xws/DvfjCJr7SIgzzTNx0zTrG0e8fMccHX3Rdz5fKwD6QS9NQeD8nAL5eL9lIttysfKx4BycithwE9N03zQNM3G5np4FRhzkGUD/fhwJO2GPsDTpmk+1Fx/a4A3cHg76uQ2wDXYd7KsMU2zGruzNA44qVsK04qP5UoE7jZN8z+maTaZpvkp8Cl+to93cjvFL9ZVB8t0ORAK/KOLwzwSndWW8ov11Ky9ZeoR+1Ozzmrr+dN6giMvV5fsU06PaG+5Er6q1XurABf2VYj3D/YhwzCeB2Y2f/Zh7I3a27WhdqoJwE7TNItbvbcce5TEYGBzm2Xfa/P55cAJXRph1/OlDgBiDMN4HTgGqAL+aJrm37sl0i5kmuZTAIZhHG7RQN0OfKkDCNztoAz7IN9aBnCw25MmYK/71pYDP+iC0LqNj3UABEQucFpvzcGgPNxCuRjl4hbKx8rHLZSTbaY9PczTsH/UmwFcij39SVsBfXxo5lO7wTTNpcDSNt+RAexo9W8njiWd0gYwDCMCe9qo/ccB0zQbDcNYAxyFPbK1O7W7XM133ey/86Z5+07HnhqpRYZhGIuav7cQu2P4ja4L/6A6pZ3iZ+vK1zIBYBhGJHaH/Dltjq3+sJ46pS3lZ+up3WXqQftTp7T1/G09Nf//vpSL5mW7bJ9yerRSElBpmqan5Q3TNBuBSuBgV8UrgM+xh/WnA+cDtwBXdX2onSoJKG3z3r7m17bl/q5le/poQ1/qoAi7EfcXoB9wMzDXMIyTuzRC/xKo24Eves12YNgZ4nbgDwf5c6/YFg5TB4GSC5zWW3MwKA+3UC72TSBvC77oNduC8rGtt+fk5qkOGoB12Lel336QxXrD9uBru+EAhmGcjz3C8/7mt5w6lnRWGyAB+yKDv6x3X8rV1q+aP99ykWMXsBH4KdAX++LZq4ZhjOycUNuts9op/rSujnQ9XQOsbx4t3cJf1pMvetI+daT8dX/yRU/Znzqiy/apLh/RbhjGadhz/B3MZuwV1C6maS4HprZ66yPDMJ4ALgYeO+IgndHucvu4bE/SrnKZprkAWNDqrfmGYbyKvd7f6YrA/FSgbgft0lu2g+bbCRcA95mm+eJ3LBbQ28Lh6iDAckGXUg4+JOVhm3KxbwJ5W2iX3rItKB/blJPBNM3VhmGEYo9ofxz7osJ5B1m0x28PndluaPO9lwEPYo8c3AyOH0s6sw3gT+vd51gMw/gNdqfSTNM09wGYpvkPDpxK4RHDMOYAFwK3dkagPuiMdsrPfPmubuBTHM1TytxMmwuYfraefNGT9imf9ID9qV162P7ks67ep7q8o900zbf4jhVgGMZM7IcEhDRfDccwjBAgBvshKe2RxyEe2uanirCvcLXW8u+25f6uZdtbP/7Klzo4mDxgSmcG5OcCdTvoqDwCaDswDGM29kO2fmWa5nednAb0ttDOOjiYPHpeLuhyysHfSXnYplzsm0DeFjoqjwDaFpSPbcrJ3zBN0wI2GoZxK/C5YRhpzVPLtAiI7aEr2g2GYdwO3AicZNrPMjiUPLr+WNJZbYB9gPc7/r6m42H6zKec3jy9xRPY0xsdY5rmxsN8fx72yNbu1FntFH9aV0dSpmnYDyE+6LSObeTR/evJFz1pn2q3HrI/dVQe/rc/Haku3aecnjpmBfY8b+NbvTcR8PDtOQ8xDONcwzCuafN2DvZTbnuSr4H+hmGktXpvEvbBpW1ZvsauE9os+0XXhdct2l0HhmFcbdhPEW6tJ673jgjU7aDdAn07MAxjMjAPuPgwJ7MBuy20tw4CKBc4rbfmYFAebqFc7JtA3hbaLdC3BeVjm3Ly/rIta/N2yzyujW3eD+jtoZlP7QYAwzBuwH5A8NS2newOHks6pQ1gmmYdsLb13w3DCMN+WK4T692XcgHch/3wwKPbdgoahnG7YRjHt1neif26U9opfraufF1PAGcCH5qmWd/6TT9aT77oSfuUL3rC/tRuPWh/OlJduk85+jBU0zSLDcN4BfijYRgXYnf8/wl4zjTNUoDmSeifMk3zBey58e4zDGMr9oMFZmA/qOdSB8I/YqZprjAM4wvgnubGRxL2XH+PmKZpGYaxEbjaNM3F2FfFlhuG8QPgbeB07Ksv1zkTfefwsQ7CsG/ZyMWeJ+oc4BTsA1nA6g3bweH0lu3AMIxg4Cngd6Zpvn6Qv7c+Dj4P/M4wjOuAf2JfVb4Quy56LB/rICBygdN6aw4G5eEWysWH11u2hcPpLduC8rFNOXm/z4AhzVMB3Is9cvsO4DPTNEt62/HB13aDYRgDgbuB6S3TxbThyLGkk9sAj2IfBxYA24A7gd3Awq4sw8H4Ui7DMI4GfgyMME2z8CBfl4Q9H/MZwHbs8g7BPi50m05up/jFuvKxTC3GY1/oassv1tPh9NR96lB64v50OD1xf2oPJ/YpRzvam12NvZI2Y18hfxW4odXfB2NPto9pmq8bhnET9oT0mUAB8FPTNP/TrRF3jnOwDzK7gRrgGeyGCtjz/0UDmKa53jCMHwJ/xn7C/WbgLNM0t3R3wF2gXXUAPITdsP039gMJtgFnmvaT7Hs0wzBMIAtwA8GGYdS1/Ilesh20tw4I4O0AO2ENB/5iGMZf2vzN4MDjYJFhGKdi18d9QD5wjWman3RjvF3BlzoIpFzgtN6ag0F5uIVysXIxoHzcTPnYppwMmKa52zCMWdgP7/w19oNfPwR+0rxIrzk+tNLudgNwERCJPdVO6+/YbpqmgbPHkk5pA5im+aRhGH2wpx+Ix744c1rL1DoOaG9O/3Hz71varJtPTNOcxTdzES/CfrjhWuAE0zR3dmXw36FT2il+tq7aW6YWadjH1rb8Zj11VlvKn9aTD+2iHrM/dVZbz5/WE/hUrhZduk+5LMvyZXkREREREREREREREWnF6TnaRURERERERERERER6NHW0i4iIiIiIiIiIiIh0gDraRUREREREREREREQ6QB3tIiIiIiIiIiIiIiIdoI52EREREREREREREZEOUEe7iIiIiIiIiIiIiEgHqKNdRERERERERERERKQD1NEuIiIiIiIiIiIiItIB6mgXEREREREREREREemA/wetdALi2lMvigAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1490.4x331.2 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace, var_names=['difference of means','difference of stds', 'effect size'],\n",
    "                  ref_val=0,\n",
    "                  color='#87ceeb');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When `forestplot` is called on a trace with more than one chain, it also plots the potential scale reduction parameter, which is used to reveal evidence for lack of convergence; values near one, as we have here, suggest that the model has converged."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x417.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(trace, var_names=['group1_mean',\n",
    "                                'group2_mean']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x518.4 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(trace, var_names=['group1_std',\n",
    "                               'group2_std',\n",
    "                               'ν_minus_one']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>difference of means</th>\n",
       "      <td>1.000907</td>\n",
       "      <td>0.447062</td>\n",
       "      <td>0.005083</td>\n",
       "      <td>0.116202</td>\n",
       "      <td>1.903386</td>\n",
       "      <td>6705.057861</td>\n",
       "      <td>0.999856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>difference of stds</th>\n",
       "      <td>0.935786</td>\n",
       "      <td>0.448293</td>\n",
       "      <td>0.005470</td>\n",
       "      <td>0.079956</td>\n",
       "      <td>1.834590</td>\n",
       "      <td>6639.138512</td>\n",
       "      <td>0.999903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>effect size</th>\n",
       "      <td>0.595007</td>\n",
       "      <td>0.280859</td>\n",
       "      <td>0.003343</td>\n",
       "      <td>0.076504</td>\n",
       "      <td>1.169303</td>\n",
       "      <td>6778.808908</td>\n",
       "      <td>0.999864</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         mean        sd  mc_error   hpd_2.5  hpd_97.5  \\\n",
       "difference of means  1.000907  0.447062  0.005083  0.116202  1.903386   \n",
       "difference of stds   0.935786  0.448293  0.005470  0.079956  1.834590   \n",
       "effect size          0.595007  0.280859  0.003343  0.076504  1.169303   \n",
       "\n",
       "                           n_eff      Rhat  \n",
       "difference of means  6705.057861  0.999856  \n",
       "difference of stds   6639.138512  0.999903  \n",
       "effect size          6778.808908  0.999864  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.summary(trace, varnames=['difference of means', 'difference of stds', 'effect size'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "1.\tGoodman SN. Toward evidence-based medical statistics. 1: The P value fallacy. Annals of Internal Medicine. 1999;130(12):995-1004. doi:10.7326/0003-4819-130-12-199906150-00008.\n",
    "2.\tJohnson D. The insignificance of statistical significance testing. Journal of Wildlife Management. 1999;63(3):763-772.\n",
    "3.\tKruschke JK. Bayesian estimation supersedes the t test. J Exp Psychol Gen. 2013;142(2):573-603. doi:10.1037/a0029146."
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    "The original pymc2 implementation was written by Andrew Straw and can be found here: https://github.com/strawlab/best\n",
    "\n",
    "Ported to PyMC3 by [Thomas Wiecki](https://twitter.com/twiecki) (c) 2015, updated by Chris Fonnesbeck."
   ]
  }
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